Levels 301 to 400

Geometry Logic Grammar

Seminar

• Niccolò Machiavelli, Discourses: Book 1, selections

Tutorial: Mathematics

Descartes: problems solved by plane geometry, and the unit. Using the constructions of Book 1, set yourself six problems (such as a product, a quotient or a square root of lengths you choose), solve each by construction, write the unit of each length beside each step, then restate each solution in one sentence.

• René Descartes, Geometry: Book 1

Acts

Examine the reasons, Check it against evidence, Express it truly

Pass when: Restate Book 1 of the Discourses in one page, naming the main claim about how a city is founded and kept. Solve the six problems from the practice step and check each answer by a second method. Then write about 1,500 words judging between Machiavelli and Plato on the best way to found a city, using passages you can reopen in both texts. You pass when every claim in your essay can be found in a passage you reopen, and your six solutions come out the same when you work them again alone.

On the site: Geometry: Apollonius' Conic Sections

Grammar Logic

Seminar

• Niccolò Machiavelli, Discourses: Books 2-3, selections

Tutorial: Language

French: sounds, spelling and reading aloud. Read one page of French aloud each day for ten days, noting each sound you find hard to say, then read a short passage twice and list the words whose spelling does not match their sound.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Read a French passage of about 150 words aloud without help, then summarise the argument of Books 2-3 of the Discourses in about 300 words. Then write about 1,500 words judging between Machiavelli and Thucydides on whether a state is held by fear or by the consent of its citizens, using passages from both texts that you can reopen. You pass when a recording of your reading, played beside a native speaker's recording of the same passage, shows no sound you can hear differing, and each claim in the essay points to a passage you reopen.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic Grammar

Seminar

• William Shakespeare, Richard II: the whole play

Tutorial: Laboratory

Galileo: falling bodies, and a ramp experiment of your own. Read the selections on falling bodies, then roll a ball down a board ramp of fixed length at three angles, ten runs each, and record the time of every run.

• Galileo, Selected writings: on falling bodies

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Restate the main conflict of Richard II in one page without the play open. Using the ramp, time the rolls at three angles, ten runs each, and table the mean and spread of each angle. Then write about 1,500 words judging between Shakespeare's Richard and Machiavelli's Discourses on whether a ruler who has lost the trust of his people can keep power by force, citing scenes you can reopen. You pass when your table repeats within its spread on a second set of runs and every claim in your essay names a scene.

On the site: Hypotheses, Predictions and Tests

Geometry Logic

Seminar

• William Shakespeare, Henry IV: Part 1

Tutorial: Mathematics

Descartes: the nature of curved lines. Read Book 2 of the Geometry, then for each curve it treats draw the curve with a string and compass or a plotted table, and write in one sentence how the curve is generated and why it counts as geometrical.

• René Descartes, Geometry: Book 2

Acts

Examine the reasons, Check it against evidence, Express it truly

Pass when: Draw two curves that Book 2 treats, from the practice step, and state the rule that generates each. Then write about 1,500 words judging between Shakespeare's Prince Hal and Machiavelli's Discourses on whether a ruler gains by a reputation for surprising his people, using scenes and passages you can reopen. You pass when each drawn curve follows its stated rule when you trace it again, and each claim in the essay points to a scene in Part 1.

On the site: Geometry: Apollonius' Conic Sections

Grammar Logic

Seminar

• William Shakespeare, Henry IV: Part 2

Tutorial: Language

French: articles, nouns, gender and agreement. Write the definite, indefinite and partitive articles with twenty nouns of your choice, marking the gender of each, then write ten short sentences with adjectives that agree in gender and number.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write ten French sentences, each with a noun and an adjective that agree in gender and number, and translate them back into English. Then write about 1,500 words judging between Shakespeare's Henry IV, Part 2, and Machiavelli's Discourses on whether a ruler's ministers can be trusted to keep order while the ruler is weak, using passages from both texts you can reopen. You pass when every noun and adjective agrees in gender and number on a check against a French grammar or dictionary, and each claim in the essay points to a passage you reopen.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Music Logic Rhetoric

Seminar

• William Shakespeare, As You Like It: the whole play

Tutorial: Music

Haydn: a string quartet followed in the score. Listen to one quartet twice while following the score, marking each change of theme, then sing the first theme aloud and name the key of each section.

• Haydn, Selected string quartets: one quartet

Acts

Understand exactly, Check it against evidence, Express it truly

Pass when: Follow one Haydn quartet in the score on two listenings, marking every return of the first theme and the key of each section, and sing the first theme aloud from memory. Then write about 1,500 words judging between Shakespeare's As You Like It and Aristotle's Ethics on whether a good life depends on fortune, using passages you can reopen in both texts. You pass when your marks match the score on a third listening and each claim in the essay names a passage you reopen.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Geometry Logic

Seminar

• William Shakespeare, Hamlet: Acts 1-3

Tutorial: Mathematics

Descartes: solid and supersolid problems. Read the selections on solid and supersolid problems, then solve four of them by conic sections, drawing each conic and checking each answer by substitution.

• René Descartes, Geometry: Book 3, selections

Acts

Examine the reasons, Check it against evidence, Express it truly

Pass when: Solve four problems from the practice step by conic sections, drawing each conic and checking each answer by substitution. Then write about 1,500 words judging between Shakespeare's Hamlet, Acts 1-3, and Sophocles' Oedipus Rex on whether a person who suspects a wrong should act at once or wait for proof, using passages you can reopen. You pass when each solution satisfies its equation when you substitute it, and each claim in the essay names a passage from one of the two texts.

On the site: Geometry: Apollonius' Conic Sections

Arithmetic Logic

Seminar

• William Shakespeare, Hamlet: Acts 4-5

Tutorial: Laboratory

Galileo: the path of a projectile. Launch a small ball from a table at three speeds, mark where it lands, and measure the horizontal distance of each landing from the table edge.

• Galileo, Selected writings: on projectiles

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Launch a ball from a table three times at each of three speeds, measure each landing, and record a table of horizontal distances. Then write about 1,500 words judging between Shakespeare's Hamlet, Acts 4-5, and Plato's Republic on whether a person's death can show whether their life was just, using passages you can reopen. You pass when your table repeats within a stated error on a second set of launches and every claim in the essay names a scene or a passage.

On the site: Hypotheses, Predictions and Tests

Rhetoric Logic Grammar

Seminar

• William Shakespeare, Othello: the whole play

Tutorial: Writing and speaking

Writing: the structure of an extended argument. Outline an argument of six points, each with a claim and a reason, then turn the outline into a 600-word essay and cut it by one third.

Acts

Examine the reasons, Express it truly

Pass when: Outline the main argument of Othello in six points, each with a claim and a reason you can reopen in the play. Then write about 1,500 words judging between Shakespeare's Othello and Aristotle's Ethics on whether a fault of character or outside pressure ruins a person, revising once after reading your draft aloud to a listener. You pass when a listener can state your thesis after one reading and every reason in the essay can be found in the text.

On the site: Technical Writing as Reasoning

Grammar Logic

Seminar

• William Shakespeare, Macbeth: the whole play

Tutorial: Language

French: the present tense and the common irregular verbs. Conjugate the present of être, avoir, aller, faire, pouvoir, vouloir and prendre aloud, then write ten sentences, each using one of these verbs in the present, and say each sentence aloud.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Conjugate seven common irregular French verbs in the present from memory, and write one sentence with each. Then write about 1,500 words judging between Shakespeare's Macbeth and Thucydides on whether ambition can be checked from within or only from outside, using passages in both texts that you can reopen. You pass when all seven conjugations are correct on a second writing and every claim in your essay points to a passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Geometry Logic

Seminar

• William Shakespeare, King Lear: Acts 1-3

Tutorial: Mathematics

Analytic geometry: the equations of the line and of the conics. Write the equation of a line through two given points, then the standard equations of a circle, an ellipse and a parabola, and check each by substituting a point you chose.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Write the equation of a line through two points you choose, and the standard equations of a circle, an ellipse and a parabola, and check each by substituting a point you chose. Then write about 1,500 words judging between Shakespeare's King Lear, Acts 1-3, and Aristotle's Ethics on whether a parent can misjudge a child's love out of pride, using passages you can reopen. You pass when every point you substituted lies on its curve and each claim in the essay names a passage.

On the site: Geometry: Apollonius' Conic Sections

Logic Arithmetic

Seminar

• William Shakespeare, King Lear: Acts 4-5

Tutorial: Evidence and inquiry

Economics today: incentives and strategic interaction. Read the units on incentives and strategic interaction, then choose one choice you can observe, such as two shops setting prices, and write its payoff table with each player's best reply.

• CORE Econ, The Economy 2.0: the units on incentives and strategic interaction

Acts

Examine the reasons, Check it against evidence, Act and review

Pass when: Build a payoff table for two sellers choosing a price, and find each seller's best reply and any stable outcome. State what the model predicts about one real choice before you check it, then check it. Then write about 1,500 words judging between the model and Shakespeare's King Lear, Acts 4-5, on whether self-interest can explain loyalty, using the model and passages you can reopen. You pass when your table recomputes to the same replies and the prediction you wrote down came before your check.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Geometry Logic

Seminar

• William Shakespeare, The Tempest: the whole play

Tutorial: Mathematics

Synthetic and analytic methods compared on one problem. Solve one plane problem first by a Euclidean construction and then by coordinates, and write one paragraph saying what each method shows and what it hides.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Solve one plane problem twice, once by a construction and once by coordinates, and write a paragraph on what each method shows and hides. Then write about 1,500 words judging between Shakespeare's The Tempest and Plato's Republic on whether knowledge should come from inherited opinion or from one's own inquiry, using passages from both texts you can reopen. You pass when both solutions agree and each claim in the essay names a passage.

On the site: Geometry: Apollonius' Conic Sections

Arithmetic Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 1, chapters 1-17

Tutorial: Laboratory

Falling and rolling: measure acceleration on an incline and account for your error. Roll a ball down a board at a set angle, time it over a fixed distance ten times, and work out the average acceleration and its error from the spread.

Acts

Check it against evidence, Examine the reasons, Express it truly

Pass when: Roll a ball down a board at a fixed angle over a measured distance ten times, time each run, and work out the average acceleration and its error from the spread. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 1, chapters 1-17, and Plato's Republic on whether a mind fed on imitations mistakes them for the world, using passages you can reopen. You pass when your error range contains your average on a repeat set of runs, and each claim in the essay names a passage from the chapters.

On the site: Hypotheses, Predictions and Tests

Grammar Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 1, chapters 18-35

Tutorial: Language

French: the past tenses: passé composé, imparfait and passé simple. Write twenty sentences, five each in passé composé, imparfait and passé simple, then mark which tense you used for each action and why.

Acts

Understand exactly, Express it truly, Examine the reasons

Pass when: Write twenty French sentences that use the passé composé, imparfait and passé simple in turn, and name the tense you used for each action. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 1, chapters 18-35, and Aristotle's Poetics on whether a fiction can teach a reader true things about the world, using passages you can reopen. You pass when a listener who knows French accepts every tense in your sentences and each claim in the essay names a passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 1, chapters 36-52

Tutorial: Mathematics

Calculus foundations: Aristotle on the continuous and the infinite. Read the selections on continuity, then write a short account of what Aristotle means by a continuous magnitude, and divide a line segment into parts that each carry a stated fraction of it.

• Aristotle, Galileo and Leibniz, Foundational readings for the calculus: selections from Aristotle on continuity

Acts

Examine the reasons, Check it against evidence, Express it truly

Pass when: Write a one-page account of what Aristotle means by a continuous magnitude, and divide a line segment into parts of stated fractions, checking that the parts add to the whole. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 1, chapters 36-52, and Aristotle on whether the infinite can be counted or only approached, using passages you can reopen. You pass when your fractions add to the whole and each claim in the essay can be checked against a text.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 2, chapters 1-25

Tutorial: Language

French: object pronouns and their order. Rewrite twenty sentences, replacing each direct and indirect object with the correct pronoun in its right place, and say each rewritten sentence aloud.

Acts

Understand exactly, Express it truly, Examine the reasons

Pass when: Rewrite twenty French sentences with direct and indirect object pronouns in their right order, and say each aloud. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 2, chapters 1-25, and Plato's Republic on whether a book's fame changes whether its account of the world is true, using passages you can reopen. You pass when a listener finds no error in the pronouns and each claim in the essay names a passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 2, chapters 26-50

Tutorial: Mathematics

Calculus foundations: Galileo on uniformly accelerated motion. Read the selections on motion, then make a table of distance against time for a body whose speed rises by equal steps in equal intervals, and state the pattern you find in the numbers.

• Aristotle, Galileo and Leibniz, Foundational readings for the calculus: selections from Galileo on motion

Acts

Check it against evidence, Examine the reasons, Express it truly

Pass when: Make a table of distance against time for a body whose speed rises by equal steps in equal intervals, and state the pattern you find in the numbers. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 2, chapters 26-50, and Galileo on whether a mind can test an idea against experience, using passages you can reopen. You pass when a second person can reproduce your table from your stated steps and your pattern holds for every row.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Arithmetic Logic

Seminar

• Miguel de Cervantes, Don Quixote: Part 2, chapters 51-74

Tutorial: Laboratory

Huygens: the motion of bodies by impact. Read the treatise, then set two balls or carts of different mass to collide, record the speeds before and after each impact, and compare the total of mass times speed before and after.

• Christiaan Huygens, On the Movement of Bodies by Impact: the treatise

Acts

Check it against evidence, Examine the reasons, Express it truly

Pass when: Collide two balls of different mass, record their speeds before and after each impact, and compare the total of mass times speed before and after. Then write about 1,500 words judging between Cervantes' Don Quixote, Part 2, chapters 51-74, and Huygens on whether a claim about the world must be tested by an impact, using passages you can reopen. You pass when your totals agree within your measurement error on three collisions, and each claim in the essay points to a passage or a measurement.

On the site: Hypotheses, Predictions and Tests

Music Logic

Seminar

• Francis Bacon, Novum Organum: Book 1, the idols

Tutorial: Music

Haydn: sonata form heard. Listen to a second quartet while following the score, marking the exposition, development and recapitulation, and name the theme that returns in the recapitulation.

• Haydn, Selected string quartets: a second quartet

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Follow a second Haydn quartet in the score, marking the exposition, development and recapitulation, and name the theme that returns. Then write about 1,500 words judging between Bacon's Novum Organum, Book 1, on the idols, and Cervantes' Don Quixote on whether a mind keeps false beliefs because of its habits, using passages you can reopen. You pass when your section marks match the score on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Arithmetic Logic

Seminar

• Francis Bacon, Novum Organum: Book 2, selections

Tutorial: Mathematics

Calculus foundations: Leibniz's differentials. Read the selections from Leibniz, then take the function y equal to x squared and write its difference quotient for three steps you choose, and say what the quotient approaches as the step shrinks.

• Aristotle, Galileo and Leibniz, Foundational readings for the calculus: selections from Leibniz

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Take the function y equal to x squared, write its difference quotient for three steps you choose, and say what the quotient approaches as the step shrinks. Then write about 1,500 words judging between Bacon's Novum Organum, Book 2, and Leibniz on whether a method of discovery can be worked out like a calculus, using passages you can reopen. You pass when your three quotients follow the pattern you state and each claim in the essay can be found in the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• René Descartes, Rules for the Direction of the Mind: selections

Tutorial: Language

French: the future and the conditional. Write twenty sentences, ten in the future and ten in the conditional, using the irregular stems of verbs such as être, avoir and aller, and say each one aloud.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write twenty French sentences in the future and the conditional, with the irregular stems correct, and say each aloud. Then write about 1,500 words judging between Descartes' Rules for the Direction of the Mind and Bacon's Novum Organum on whether a rule of method can replace long experience, using passages you can reopen. You pass when every stem is correct on a second writing and each claim in the essay points to a rule or an aphorism in the text.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• René Descartes, Discourse on Method: the whole work

Tutorial: Mathematics

Calculus: continuity. Define a continuous function in your own words, then decide for five graphs or formulas whether each is continuous at a point you choose, and give the reason for each decision.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Decide, for five functions you draw or write, whether each is continuous at a point you choose, and give the reason for each decision with the test you used. Then write about 1,500 words judging between Descartes' Discourse on the Method and Aristotle's account of the continuous on whether a method can divide a problem into parts without losing the whole, using passages you can reopen. You pass when a reader can check each decision with the same test and the essay's claims point to passages in both texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Arithmetic Logic

Seminar

• René Descartes, Meditations: Meditations 1-3

Tutorial: Laboratory

Collisions: test the conservation of quantity of motion with two carts or coins. Set two carts of stated masses to collide five times, record their velocities before and after each collision, and compute the total of mass times velocity for each run.

Acts

Check it against evidence, Examine the reasons, Express it truly

Pass when: Collide two carts of stated masses five times, record their velocities before and after, and compute the total of mass times velocity for each run. Then write about 1,500 words judging between Descartes' Meditations 1-3 and Bacon's Novum Organum on whether the senses mislead the mind, using passages you can reopen. You pass when the totals agree within your measurement error in four of five runs and each claim in the essay names a passage from one of the two texts.

On the site: Hypotheses, Predictions and Tests

Grammar Logic

Seminar

• René Descartes, Meditations: Meditations 4-6

Tutorial: Language

French: the subjunctive. Write twenty sentences that need the subjunctive after verbs of wanting, doubt and feeling, and say each sentence aloud with its trigger named.

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write twenty French sentences that use the subjunctive after verbs of wanting, doubt and feeling, and name the trigger in each. Then write about 1,500 words judging between Descartes' Meditations 4-6 and Plato's Republic on whether reason can reach what is true without the senses, using passages you can reopen. You pass when every subjunctive is correct on a second writing and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Rhetoric Logic

Seminar

• Elisabeth of Bohemia and René Descartes, Selected correspondence: selected correspondence

Tutorial: Writing and speaking

Speaking: explain a proof aloud to a newcomer. Choose one proof from the Geometry or the Meditations, and explain it aloud to a listener who has not read it, in under ten minutes, without showing the page.

Acts

Express it truly, Examine the reasons

Pass when: Explain one proof from the Geometry or the Meditations aloud to a listener who has not read it, in under ten minutes, without the page. Then write about 1,500 words judging between the selected letters of Elisabeth and Descartes and Plato's Republic on whether a teacher owes a full answer to a student's objection, using passages you can reopen. You pass when your listener can restate the proof in their own words and your essay answers each objection raised in the letters.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Arithmetic Logic

Seminar

• Blaise Pascal, Pensées: selections, first part

Tutorial: Mathematics

Calculus: infinity and infinitesimals. Add the first ten terms of a series whose terms halve each time, and state in your own words what it means for a sum to have a limit.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Add the first ten terms of a series whose terms halve each time, state what the sum approaches, and explain in one page what it means for a sum to have a limit. Then write about 1,500 words judging between Pascal's Pensées, first part, and Aristotle on whether infinity can be known by reason, using passages you can reopen. You pass when your partial sums match the table you computed, and each claim in the essay points to a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• Blaise Pascal, Pensées: selections, second part

Tutorial: Language

French: analysing a long sentence into clauses and their relations. Take five long sentences from the selections, mark each main clause, subordinate clause and relative link, and rewrite each as two or three short sentences in English.

Acts

Understand exactly, Examine the reasons

Pass when: Mark the clauses and their relations in five long French sentences from the selections, and rewrite each as two or three short English sentences. Then write about 1,500 words judging between Pascal's Pensées, second part, and Bacon on whether a long argument can be trusted when it is hard to follow, using passages you can reopen. You pass when a listener can follow each rewritten sentence and every claim in the essay names a passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Blaise Pascal, Pensées: selections, third part

Tutorial: Laboratory

Periodic motion: the pendulum, its period and its length. Hang a pendulum at three lengths, time twenty swings for each, and plot the period against the length on squared paper.

Acts

Check it against evidence, Examine the reasons

Pass when: Time twenty swings of a pendulum at each of three lengths, work out the period for each, and plot period against length on squared paper. Then write about 1,500 words judging between Pascal's Pensées, third part, and Plato's Republic on whether a careful observer can read the order of nature, using passages you can reopen. You pass when your three periods repeat within your timing error and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Arithmetic Logic

Seminar

• Thomas Hobbes, Leviathan: Part 1, selections

Tutorial: Mathematics

Calculus: limits. Compute the limit of (x squared minus one) divided by (x minus one) as x approaches one, by factoring and by a table of values near one, then say in one paragraph why the two methods agree.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Find the limit of (x squared minus one) divided by (x minus one) as x approaches one, by factoring and by a table of values, and say in one paragraph why the two methods agree. Then write about 1,500 words judging between Hobbes' Leviathan, Part 1, and Descartes' Discourse on whether reasoning from definitions can establish what is true about human beings, using passages you can reopen. You pass when your table of values approaches the factored answer and each claim in the essay can be found in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Logic Arithmetic

Seminar

• Thomas Hobbes, Leviathan: Part 2, selections

Tutorial: Evidence and inquiry

Economics today: firms and markets. Read the units on firms and markets, then choose one local market you can observe and record its sellers, buyers and prices over three visits.

• CORE Econ, The Economy 2.0: the units on firms and markets

Acts

Examine the reasons, Check it against evidence, Act and review

Pass when: Observe one local market on three visits and record the sellers, buyers and prices, then state what the model of firms and markets predicts about each price before you compare. Then write about 1,500 words judging between Hobbes' Leviathan, Part 2, selections, and Plato's Republic on whether a city's order can depend on trade and exchange, using passages you can reopen. You pass when your predictions were written before you checked the prices and each claim in the essay can be traced to a record or a passage.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Music Logic

Seminar

• Thomas Hobbes, Leviathan: Parts 3-4, selections

Tutorial: Music

Mozart: Don Giovanni, Act 1. Listen to Act 1 while following the libretto, and mark where each number begins and ends, naming the key of each.

• Mozart, Don Giovanni: Act 1

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Listen to Act 1 of Don Giovanni while following the libretto, marking where each number begins and ends and naming its key. Then write about 1,500 words judging between Hobbes' Leviathan, Parts 3-4, selections, and Plato's Republic on whether the rulers of a city should also decide what its people may believe about the gods, using passages you can reopen. You pass when your list of numbers matches the score on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Arithmetic Logic

Seminar

• Baruch Spinoza, Theologico-Political Treatise: selections, first part

Tutorial: Mathematics

Calculus: limits, worked. Work through ten limit problems from a textbook of your choice, writing every step, and check each answer with a table of values near the point.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Work ten limit problems, writing every step, and check each answer with a table of values near the point. Then write about 1,500 words judging between Spinoza's Theological-Political Treatise, first part, and Bacon on whether Scripture can be read by the same rules as nature, using passages you can reopen. You pass when at least nine answers match their tables and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Rhetoric

Seminar

• Baruch Spinoza, Theologico-Political Treatise: selections, second part

Tutorial: Language

French: false friends, idiom and diction. List twenty French words that look like English words but mean something else, check each meaning in a French dictionary, and write one correct sentence with each.

Acts

Understand exactly, Express it truly

Pass when: List twenty French false friends, check each meaning in a French dictionary, and write one correct sentence with each. Then write about 1,500 words judging between Spinoza's Treatise, second part, and Plato's Republic on whether a state can allow free speech without losing its peace, using passages you can reopen. You pass when every sentence is correct on a second check and the essay names a passage for each claim.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Baruch Spinoza, Ethics: Part 1

Tutorial: Laboratory

Leibniz: living force against quantity of motion. Read the essay, then use two carts of one mass at two speeds to compute what each measure predicts, mass times speed and mass times speed squared, and record their ratios.

• Leibniz, Essay on Dynamics: the essay

Acts

Check it against evidence, Examine the reasons

Pass when: Using two carts of one mass at two speeds, compute both measures, mass times speed and mass times speed squared, and record their ratios. Then write about 1,500 words judging between Spinoza's Ethics, Part 1, and Leibniz's essay on whether substance and force are one thing or two, using passages you can reopen. You pass when your ratios match the predictions of each measure within your error, and each claim in the essay names a passage in the Ethics or the essay.

On the site: Hypotheses, Predictions and Tests

Arithmetic

Seminar

• Baruch Spinoza, Ethics: Part 2

Tutorial: Mathematics

Calculus: rates of change. Find the average rate of change of x cubed between x equal to one and x equal to two, then estimate the rate at x equal to one from a table of smaller and smaller intervals.

Acts

Understand exactly, Check it against evidence

Pass when: Find the average rate of change of x cubed between one and two, then estimate the rate at one from a table of smaller and smaller intervals. Then write about 1,500 words judging between Spinoza's Ethics, Part 2, and Plato's Republic on whether knowledge of a whole can be built from its parts, using passages you can reopen. You pass when your table approaches the value your algebra gives and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• Baruch Spinoza, Ethics: Parts 3-4, selections

Tutorial: Language

French: La Rochefoucauld's maxims, translated and weighed. Translate twelve maxims into English, then write beside each a short note on whether the maxim holds and where it claims too much.

• La Rochefoucauld, Maxims: selected maxims

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Translate twelve maxims from La Rochefoucauld into English and write beside each a note on whether it holds and where it claims too much. Then write about 1,500 words judging between Spinoza's Ethics, Parts 3-4, selections, and La Rochefoucauld on whether human beings act from self-love, using passages from both that you can reopen. You pass when a second reader can check each translation against the French and every claim in the essay names a passage.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Baruch Spinoza, Ethics: Part 5

Tutorial: Mathematics

Calculus: the derivative. Find the derivative of x squared and of x cubed from first principles, then check each against a table of difference quotients at x equal to two.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Find the derivative of x squared and of x cubed from first principles, then check each against a table of difference quotients at x equal to two. Then write about 1,500 words judging between Spinoza's Ethics, Part 5, and Plato's Republic on whether a person can reach a lasting good by reason alone, using passages you can reopen. You pass when both derivatives match the table and each claim in the essay names a passage from one of the two texts.

On the site: The Academy: Proofs, Definitions and the Method of Reason

Arithmetic Logic

Seminar

• Gottfried Wilhelm Leibniz, Discourse on Metaphysics: the whole work

Tutorial: Laboratory

Work, kinetic energy and potential energy, from the dispute to the definitions. Lift a mass through a measured height, record the work you do, then compare the energy at the top and bottom of its fall, writing each definition in your own words.

Acts

Check it against evidence, Examine the reasons

Pass when: Lift a mass through a measured height, record the work you do, then compare the energy at the top and bottom of its fall, and write each definition in your own words. Then write about 1,500 words judging between Leibniz's Discourse on Metaphysics and Descartes on whether the same quantity of motion is kept in the world, using passages you can reopen. You pass when the work you measured matches the energy change within your error and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Arithmetic Logic

Seminar

• Gottfried Wilhelm Leibniz, Monadology: the whole work

Tutorial: Mathematics

Calculus: the rules of differentiation. Differentiate ten functions using the sum, product, quotient and chain rules, writing the rule you used at each step.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Differentiate ten functions by the sum, product, quotient and chain rules, naming the rule used at each step. Then write about 1,500 words judging between Leibniz's Monadology and Spinoza's Ethics on whether the world is a single order of parts, using passages you can reopen. You pass when at least nine derivatives agree with a second method you choose, and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• John Milton, Paradise Lost: Book 1

Tutorial: Language

French: the maxim as a form of argument. Write ten French maxims of your own, each with a claim, a reason and an example, then read further maxims by La Rochefoucauld aloud, marking the claim in each.

• La Rochefoucauld, Maxims: further maxims

Acts

Understand exactly, Examine the reasons, Express it truly

Pass when: Write ten French maxims, each with a claim, a reason and an example, and read further maxims by La Rochefoucauld aloud, marking the claim in each. Then write about 1,500 words judging between Milton's Paradise Lost, Book 1, and La Rochefoucauld on whether pride is the root of human action, using passages you can reopen. You pass when each maxim has a claim and reason that a listener can state, and every claim in the essay names a passage in one of the two texts.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Rhetoric Grammar

Seminar

• John Milton, Paradise Lost: Book 2

Tutorial: Writing and speaking

Writing: a translation from the French with a commentary. Translate a page of French prose into English, then write a commentary of about two hundred words on three choices you made in the translation.

Acts

Express it truly, Examine the reasons

Pass when: Translate a page of French prose into English and write a commentary of about two hundred words on three choices you made. Then write about 1,500 words judging between Milton's Paradise Lost, Book 2, and Bacon on whether a fine style can make a false argument persuasive, using passages you can reopen. You pass when the translation can be checked against the French and a listener can name your three choices from the commentary.

On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech

Arithmetic Geometry

Seminar

• John Milton, Paradise Lost: Book 3

Tutorial: Mathematics

Calculus: differentiation applied to motion and to curves. Find the velocity of an object whose position follows a quadratic formula you choose, and the slope of its curve at one point, writing each step.

Acts

Understand exactly, Check it against evidence

Pass when: Find the velocity of an object whose position follows a quadratic formula you choose, and the slope of its curve at one point, writing every step. Then write about 1,500 words judging between Milton's Paradise Lost, Book 3, and Plato's Republic on whether the order of heaven is a fit model for a human city, using passages you can reopen. You pass when your velocity and slope match a numerical check at the same point and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Music Logic

Seminar

• John Milton, Paradise Lost: Book 4

Tutorial: Music

Mozart: Don Giovanni, Act 2. Listen to Act 2 while following the libretto, mark each number, and name the voice that leads it.

• Mozart, Don Giovanni: Act 2

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Listen to Act 2 of Don Giovanni while following the libretto, mark each number, and name the voice that leads it. Then write about 1,500 words judging between Milton's Paradise Lost, Book 4, and Aristotle's Ethics on whether a fallen creature can still choose the good, using passages you can reopen. You pass when your list of numbers and leading voices matches the score on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Grammar Rhetoric

Seminar

• John Milton, Paradise Lost: Book 5

Tutorial: Language

French: Pascal's prose. Read a passage of Pascal's prose aloud in French, then copy it by hand and write your English version beside it, comparing it with a published translation.

• Blaise Pascal, Pensées: selected fragments, in French

Acts

Understand exactly, Express it truly

Pass when: Read a passage of Pascal in French aloud, copy it by hand, and write your English version beside it. Then write about 1,500 words judging between Milton's Paradise Lost, Book 5, and Pascal on whether a temptation is best resisted by argument or by grace, using passages you can reopen. You pass when a listener accepts your reading aloud and every claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• John Milton, Paradise Lost: Book 6

Tutorial: Laboratory

Mayer: heat and the conservation of force. Read the selections, then list the quantities they say are conserved, and write a table with a column for each source's evidence.

• Mayer, Selected writings: selections

Acts

Check it against evidence, Examine the reasons

Pass when: List the quantities that the selections say are conserved, with the evidence each source gives, in a table with one row per quantity. Then write about 1,500 words judging between Milton's Paradise Lost, Book 6, and Homer's Iliad on whether a battle can be settled by force alone, using passages you can reopen. You pass when every row of your table cites a sentence you can reopen and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Arithmetic Logic

Seminar

• John Milton, Paradise Lost: Book 7

Tutorial: Mathematics

Calculus: the integral as a sum. Approximate the area under y equal to x squared between zero and two by adding rectangles, first four and then eight wide, and compare each sum with the value of the integral.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Approximate the area under y equal to x squared between zero and two with four rectangles, then with eight, and compare each sum with the value of the integral. Then write about 1,500 words judging between Milton's Paradise Lost, Book 7, and Plato's Timaeus on whether creation is best explained as an order of parts, using passages you can reopen. You pass when your eight-rectangle sum is closer to the integral than your four-rectangle sum, and each claim in the essay names a passage.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Rhetoric

Seminar

• John Milton, Paradise Lost: Book 8

Tutorial: Language

French: Descartes' plain style. Read a passage of Descartes' Discourse in French aloud, then rewrite three of its sentences in English that keep the order of his reasons and drop every word not needed.

• René Descartes, Discourse on Method: Part 1, in French

Acts

Understand exactly, Express it truly

Pass when: Read a passage of Descartes' Discourse in French aloud, then rewrite three of its sentences in plain English that keep the order of his reasons. Then write about 1,500 words judging between Milton's Paradise Lost, Book 8, and Descartes on whether a plain style can carry a deep argument, using passages you can reopen. You pass when a listener follows the order of your rewritten sentences and every claim in the essay names a passage from one of the two texts.

On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech

Arithmetic Logic

Seminar

• John Milton, Paradise Lost: Book 9

Tutorial: Mathematics

Calculus: the rules of integration. Integrate ten polynomial functions, naming the rule used for each, then differentiate each answer to check it.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Integrate ten polynomial functions, naming the rule used for each, then differentiate each answer to check it. Then write about 1,500 words judging between Milton's Paradise Lost, Book 9, and Aristotle on whether a fall can be explained by a flaw in the nature of a thing, using passages you can reopen. You pass when at least nine answers differentiate back to the original function and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Arithmetic Logic

Seminar

• John Milton, Paradise Lost: Book 10

Tutorial: Laboratory

Heat and the concept of energy: a timeline with the evidence at each step. Build a timeline of six steps from the Huygens, Leibniz and Mayer readings of Levels 319, 335 and 346, writing beside each step the evidence that moved it forward and the objection it answered.

Acts

Check it against evidence, Examine the reasons

Pass when: Build a timeline of six steps in the history of the concept of energy, from the Huygens, Leibniz and Mayer readings of Levels 319, 335 and 346, naming the evidence and the objection answered at each step. Then write about 1,500 words judging between Milton's Paradise Lost, Book 10, and Leibniz on whether a fall brings a loss of force or only a change in it, using passages you can reopen. You pass when every step names evidence you can reopen and your essay answers the strongest objection on each side.

On the site: Hypotheses, Predictions and Tests

Logic Arithmetic

Seminar

• John Milton, Paradise Lost: Book 11

Tutorial: Evidence and inquiry

Economics today: credit and externalities. Read the units on credit, banks and externalities, then pick one everyday cost that falls on someone who did not choose it, such as noise or traffic, and write how it is ignored and what would change that.

• CORE Econ, The Economy 2.0: the units on credit, banks and externalities

Acts

Examine the reasons, Check it against evidence, Act and review

Pass when: Pick one everyday cost that falls on someone who did not choose it, such as noise or traffic, and set out how the cost is ignored and what would change that. Then write about 1,500 words judging between Milton's Paradise Lost, Book 11, and Plato's Republic on whether a city's laws can make people bear the costs of their acts, using passages you can reopen. You pass when your account names who pays the cost, and each claim in the essay can be checked against a passage or a record.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Arithmetic Geometry

Seminar

• John Milton, Paradise Lost: Book 12

Tutorial: Mathematics

Calculus: integration applied to areas and volumes. Find the area between y equal to x and y equal to x squared from zero to one, then the volume of one solid of revolution you choose, writing each integral.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Find the area between y equal to x and y equal to x squared from zero to one, and the volume of one solid of revolution you choose, writing each integral. Then write about 1,500 words judging between Milton's Paradise Lost, Book 12, and Plato's Republic on whether a city can be judged by how it ends, using passages you can reopen. You pass when your area matches a numerical estimate, your volume matches its formula, and each claim in the essay names a passage in one of the texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• Gottfried Wilhelm Leibniz, Principles of Nature and Grace: the whole work

Tutorial: Language

French: the cogito in Descartes' own French. Read the cogito passage from Part 4 of the Discourse in French aloud, then write it in English, noting each word whose sense differs from its English match.

• René Descartes, Discourse on Method: Part 4, in French

Acts

Understand exactly, Examine the reasons

Pass when: Read the cogito passage from Part 4 of Descartes' Discourse in French aloud, then write it in English, noting each word whose sense differs from its English match. Then write about 1,500 words judging between Leibniz's Principles of Nature and Grace and Descartes on whether the thinking self is the first thing we can know most surely, using passages you can reopen. You pass when a listener accepts your reading aloud and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Gottfried Wilhelm Leibniz, Selected philosophical essays: selected philosophical essays

Tutorial: Mathematics

Calculus: the fundamental theorem. Compute the integral of t squared from zero to x, differentiate the result with respect to x, and check that you return to the integrand.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the integral of t squared from zero to x, differentiate the result with respect to x, and state in one paragraph how the two operations are related. Then write about 1,500 words judging between Leibniz's selected essays and Aristotle on whether a whole can be built from its parts, using passages you can reopen. You pass when the derivative returns the integrand and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Music Arithmetic

Seminar

• John Locke, Second Treatise of Government: chapters 1-5

Tutorial: Laboratory

Taylor: the vibrating string. Stretch one string at three tensions, pluck each, and record the pitch a tuner shows at each tension.

• Brook Taylor, Selected writings: selections

Acts

Check it against evidence, Understand exactly, Examine the reasons

Pass when: Stretch one string at three tensions, pluck each, and record the pitch a tuner shows at each tension, with the tension you used. Then write about 1,500 words judging between Locke's Second Treatise, chapters 1-5, and Hobbes on whether a government's power rests on natural law or on a contract, using passages you can reopen. You pass when your three pitches rise with tension in the order the selections describe and each claim in the essay names a passage in one of the two texts.

On the site: From a Vibrating String to a Proof

Grammar Rhetoric

Seminar

• John Locke, Second Treatise of Government: chapters 6-12

Tutorial: Language

French: Rousseau's prose. Read a passage of Rousseau's prose aloud in French, then write a summary of it in English in fifty words, marking three words you had to look up.

• Jean-Jacques Rousseau, Selected writings: selected prose, in French

Acts

Understand exactly, Express it truly, Examine the reasons

Pass when: Read a passage of Rousseau's prose in French aloud, then summarise it in English in fifty words, marking three words you had to look up. Then write about 1,500 words judging between Locke's Second Treatise, chapters 6-12, and Hobbes on whether those who govern may take a citizen's property without his consent, using passages you can reopen. You pass when your summary keeps the author's order of claims and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Music Logic

Seminar

• John Locke, Second Treatise of Government: chapters 13-19

Tutorial: Music

Beethoven: the Third Symphony, first and second movements. Follow the first and second movements in a score, marking the main themes and one moment in the music that surprises you.

• Beethoven, Symphony No. 3: the first and second movements

Acts

Understand exactly, Examine the reasons

Pass when: Follow the first and second movements of Beethoven's Third Symphony in a score, marking the main themes and one moment that surprises you. Then write about 1,500 words judging between Locke's Second Treatise, chapters 13-19, and Plato's Republic on whether the dissolution of a government can be just, using passages you can reopen. You pass when your theme marks match the score on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Arithmetic Logic

Seminar

• Jonathan Swift, Gulliver's Travels: Parts 1-2

Tutorial: Mathematics

Calculus: logarithms and the exponential. Compute the base-10 logarithms of 2, 10 and 100, then raise 10 to each answer to return to 2, 10 and 100, and compute e to the power 0, 1 and 2 and check each by taking its natural logarithm.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the base-10 logarithms of 2, 10 and 100, then raise 10 to each answer to return to 2, 10 and 100, and compute e to the power 0, 1 and 2 and check each by taking its natural logarithm. Then write about 1,500 words judging between Swift's Gulliver's Travels, Parts 1-2, and Plato's Republic on whether a satire of rulers can be serious, using passages you can reopen. You pass when every pair reverses to its start and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Rhetoric Logic

Seminar

• Jonathan Swift, Gulliver's Travels: Parts 3-4

Tutorial: Writing and speaking

Writing: a dialogue between two of this year's authors. Write a dialogue of about 250 words between two authors you have read this year, each arguing the strongest case for a view, then cut it by a fifth.

Acts

Express it truly, Examine the reasons

Pass when: Write a dialogue of about 250 words between two authors you have read this year, each giving the strongest case for a view, then cut it by a fifth. Then write about 1,500 words judging between Swift's Gulliver's Travels, Parts 3-4, and Shakespeare on whether a wise person can laugh at folly without contempt, using passages you can reopen. You pass when a listener can say which view each speaker holds and each claim in the essay names a passage in one of the two texts.

On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech

Grammar Rhetoric

Seminar

• David Hume, A Treatise of Human Nature: Book 1, selections on ideas and causation

Tutorial: Language

French: La Fontaine's fables read aloud. Read five fables aloud in French, then write the moral of each in one English sentence, checked against the fable.

• La Fontaine, Fables: selected fables

Acts

Understand exactly, Express it truly

Pass when: Read five La Fontaine fables aloud in French, and write the moral of each in one English sentence checked against the fable. Then write about 1,500 words judging between Hume's Treatise, Book 1, on ideas and causation, and Bacon on whether a cause can be seen or only inferred, using passages you can reopen. You pass when a listener recognises the moral of each fable from your sentences and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• David Hume, A Treatise of Human Nature: Book 1, selections on scepticism and personal identity

Tutorial: Mathematics

Calculus: logarithmic functions, worked. Differentiate the natural logarithm of x and of x cubed plus one, writing each step, and check both answers at x equal to one.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Differentiate the natural logarithm of x, and the natural logarithm of x cubed plus one, writing each step, then check both answers at x equal to one. Then write about 1,500 words judging between Hume's Treatise, Book 1, on scepticism and personal identity, and Plato's Republic on whether the self is a single thing, using passages you can reopen. You pass when both answers match a numerical check and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Music Arithmetic

Seminar

• David Hume, A Treatise of Human Nature: Books 2-3, selections on the passions and morals

Tutorial: Laboratory

Bernoulli and Euler: the vibrating-string dispute. Set the two accounts of the string's motion side by side in a table, with one row per claim and the evidence that supports it.

• Daniel Bernoulli, Selected writings: selections
• Euler, Selected writings: selections

Acts

Examine the reasons, Check it against evidence

Pass when: Set the two accounts of the vibrating string side by side in a table, with one row per claim and the evidence each gives. Then write about 1,500 words judging between Hume's Treatise, Books 2-3, on the passions and morals, and Aristotle on whether feeling can be right or wrong, using passages you can reopen. You pass when every row cites a passage in the selections that you can reopen and each claim in the essay names a passage in one of the two texts.

On the site: From a Vibrating String to a Proof

Arithmetic Logic

Seminar

• Jean-Jacques Rousseau, Discourse on the Origin of Inequality: the dedication and Part 1

Tutorial: Mathematics

Calculus: selected differential equations. Solve two first-order equations of the form dy/dx equal to k times y, one with k equal to two and one with k equal to minus one, and check each solution by differentiating it.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Solve two first-order equations of the form dy/dx equal to k times y, with k equal to two and with k equal to minus one, and check each solution by differentiating it. Then write about 1,500 words judging between Rousseau's Discourse on Inequality, the dedication and Part 1, and Hobbes on whether human beings begin in a state of war, using passages you can reopen. You pass when both solutions satisfy their equations and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Grammar Logic

Seminar

• Jean-Jacques Rousseau, Discourse on the Origin of Inequality: Part 2

Tutorial: Language

French: the fable's argument and its moral. Read a further La Fontaine fable aloud in French, then state its argument in three sentences and its moral in one, and say whether the moral follows.

• La Fontaine, Fables: further fables

Acts

Understand exactly, Examine the reasons

Pass when: Read a further La Fontaine fable aloud in French, then state its argument in three sentences and its moral in one, and say whether the moral follows. Then write about 1,500 words judging between Rousseau's Discourse on Inequality, Part 2, and Plato's Republic on whether private property begins the decline of a city, using passages you can reopen. You pass when a listener finds the moral follows from the argument, or you state where it does not, and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Jean-Jacques Rousseau, The Social Contract: Books 1-2

Tutorial: Mathematics

Calculus: differential equations of motion. Write the equation of motion for a mass on a spring, check by differentiating twice that x equal to A cos(wt), with w squared equal to k over m, satisfies it, fit A to a stated starting displacement, and sketch the position against time for one full period.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Write the equation of motion for a mass on a spring, check by differentiating twice that x equal to A cos(wt), with w squared equal to k over m, satisfies it, fit A to a stated starting displacement, and sketch the position against time for one full period. Then write about 1,500 words judging between Rousseau's Social Contract, Books 1-2, and Locke's Second Treatise on whether the general will can be a source of law, using passages you can reopen. You pass when your sketch matches the solution at five points and each claim in the essay names a passage in one of the two texts.

On the site: Calculus and Beyond: Change, Structure and Uncertainty

Music Arithmetic

Seminar

• Jean-Jacques Rousseau, The Social Contract: Books 3-4

Tutorial: Laboratory

Waves: a vibrating string measured and heard on the monochord. Stop one string at lengths of one half, two thirds and three quarters of its full length, and listen to each pitch against a tuner.

Acts

Check it against evidence, Understand exactly, Examine the reasons

Pass when: Stop one string at lengths of one half, two thirds and three quarters of its full length, record the pitch of each against a tuner, and write the ratio of each length to the full string. Then write about 1,500 words judging between Rousseau's Social Contract, Books 3-4, and Plato's Republic on whether a just city can be kept by its laws alone, using passages you can reopen. You pass when your three pitches match the ratios you wrote within a stated tolerance and each claim in the essay names a passage in one of the two texts.

On the site: From a Vibrating String to a Proof

Grammar Rhetoric

Seminar

• Adam Smith, The Wealth of Nations: Book 1, selections

Tutorial: Language

French: The Princess of Clèves, selections. Read a selection aloud in French, then write a summary of one scene in English in fifty words and mark the tense of the narration.

• Madame de La Fayette, The Princess of Clèves: selections, a variable selection

Acts

Understand exactly, Express it truly

Pass when: Read a selection of The Princess of Clèves aloud in French, then summarise one scene in English in fifty words, marking the tense of the narration. Then write about 1,500 words judging between Smith's Wealth of Nations, Book 1, selections, and Aristotle on whether a person's wants are better met by exchange or by moderation, using passages you can reopen. You pass when your summary matches the scene when you reopen it and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Geometry Arithmetic Logic

Seminar

• Adam Smith, The Wealth of Nations: Books 2-3, selections

Tutorial: Mathematics

Geometrical and analytical approaches to motion compared. Solve one motion problem by a geometric diagram and then by an equation, and write a paragraph on which method shows the cause more clearly.

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Solve one motion problem first by a geometric diagram and then by an equation, and write a paragraph saying which method shows the cause more clearly. Then write about 1,500 words judging between Smith's Wealth of Nations, Books 2-3, selections, and Descartes' Discourse on whether a system of exchange can be understood by a method like geometry, using passages you can reopen. You pass when both solutions agree on the answer and each claim in the essay names a passage in one of the two texts.

On the site: Geometry, Euclid and Trigonometry

Music Logic

Seminar

• Adam Smith, The Wealth of Nations: Book 4, selections

Tutorial: Music

Beethoven: the Third Symphony, third and fourth movements. Follow the third and fourth movements in a score, marking each return of the main theme and how the final movement ends.

• Beethoven, Symphony No. 3: the third and fourth movements

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Follow the third and fourth movements of Beethoven's Third Symphony in a score and mark each return of the main theme and how the final movement ends. Then write about 1,500 words judging between Smith's Wealth of Nations, Book 4, selections, and Plato's Republic on whether a state's wealth is a good in itself, using passages you can reopen. You pass when your marks match the score on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Logic Arithmetic

Seminar

• Adam Smith, The Wealth of Nations: Book 5, selections

Tutorial: Evidence and inquiry

Causal inference: models and their assumptions. Write a simple causal model for one question of public policy, list its assumptions, and say which assumption you would test first and how.

• Miguel Hernán and James Robins, Causal Inference: What If: Part 2, selections

Acts

Examine the reasons, Check it against evidence, Act and review

Pass when: Write a simple causal model for one question of public policy, list its assumptions, and say which assumption you would test first and how. Then write about 1,500 words judging between Smith's Wealth of Nations, Book 5, selections, and Hernán and Robins' account of causal inference on whether a government's spending can be judged by what follows when it is cut, using passages you can reopen. You pass when every assumption is written down and the test you name would show it false if it were false, and each claim in the essay names a passage.

On the site: Hypotheses, Predictions and Tests

Astronomy Logic

Seminar

• Immanuel Kant, Critique of Pure Reason: the Prefaces and the Introduction

Tutorial: Mathematics

Newton: definitions and laws of motion. Read the definitions and the laws of motion, then compute the acceleration of a body of stated mass under a stated force, using the second law in its modern form, force equals mass times acceleration, and say in one sentence how Newton's own wording differs.

• Newton, Principia: the Definitions and the Laws of Motion

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the acceleration of a body of stated mass under a stated force, using the second law in its modern form, say in one sentence how Newton's own wording differs, and check your answer by its units. Then write about 1,500 words judging between Kant's Critique of Pure Reason, Prefaces and Introduction, and Newton on whether knowledge of nature can be certain before experience, using passages you can reopen. You pass when your acceleration matches the stated law and the units agree, and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Geometry Logic

Seminar

• Immanuel Kant, Critique of Pure Reason: the Transcendental Aesthetic

Tutorial: Laboratory

Huygens: light as a wave, and his principle. Read the opening chapters, then draw the wavefronts from a point source and use Huygens' principle to construct the front a short time later, with a ruler and compass.

• Christiaan Huygens, Treatise on Light: the opening chapters

Acts

Check it against evidence, Understand exactly, Examine the reasons

Pass when: Draw the wavefronts from a point source and use Huygens' principle to construct the front a short time later, with a ruler and compass. Then write about 1,500 words judging between Kant's Transcendental Aesthetic and Newton on whether space is given before experience, using passages you can reopen. You pass when your constructed front matches the drawn circle at each point and each claim in the essay names a passage in one of the two texts.

On the site: Geometry: Apollonius' Conic Sections

Grammar Rhetoric

Seminar

• Immanuel Kant, Critique of Pure Reason: the Transcendental Analytic, selections

Tutorial: Language

French: Racine's Phèdre, Acts 1 and 2. Read Acts 1 and 2 aloud in French, then list the main verbs of each speech and their tenses, and write a two-line English summary of each speech.

• Racine, Phèdre: Acts 1-2

Acts

Understand exactly, Express it truly

Pass when: Read Acts 1 and 2 of Racine's Phèdre aloud in French, list the main verbs of each speech with their tenses, and write a two-line English summary of each speech. Then write about 1,500 words judging between Kant's Transcendental Analytic, selections, and Hume on whether the idea of cause comes from experience alone, using passages you can reopen. You pass when a listener follows your summaries and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Astronomy Arithmetic

Seminar

• Immanuel Kant, Critique of Pure Reason: the Transcendental Dialectic: the antinomies, selections

Tutorial: Mathematics

Newton: the method of first and last ratios. Read the selections on first and last ratios, then compute the ratio of the sine of a small angle to the angle for five angles that shrink toward zero, and tabulate the results.

• Newton, Principia: Book 1, Section 1, on first and last ratios

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the ratio of the sine of a small angle to the angle, in radians, for five angles that shrink toward zero, and state what the ratios approach. Then write about 1,500 words judging between Kant's antinomies and Newton's method of first and last ratios on whether a quantity can be taken to vanish without contradiction, using passages you can reopen. You pass when your five ratios approach the value you stated and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Logic

Seminar

• Immanuel Kant, Critique of Pure Reason: the Transcendental Dialectic: the ideal of pure reason, selections

Tutorial: Language

French: Phèdre, Acts 3 to 5. Read Acts 3 to 5 aloud in French, then write the sequence of decisions each character makes, in English, one line each.

• Racine, Phèdre: Acts 3-5

Acts

Understand exactly, Examine the reasons

Pass when: Read Acts 3 to 5 of Racine's Phèdre aloud in French, then write one English line for each decision a character makes, in order. Then write about 1,500 words judging between Kant's ideal of pure reason, selections, and Anselm's Proslogion on whether the idea of a most perfect being shows that it exists, using passages you can reopen. You pass when your lines follow the order of the acts and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Rhetoric Logic

Seminar

• Immanuel Kant, Groundwork of the Metaphysics of Morals: the Preface and Section 1

Tutorial: Writing and speaking

Speaking: a twenty-minute lecture on one book. Prepare a lecture of about twenty minutes on one book you have read this level, with three points and one objection, and give it aloud to a listener.

Acts

Express it truly, Examine the reasons

Pass when: Prepare and give aloud a lecture of about twenty minutes on one book you have read this level, with three points and one objection that you answer. Then write about 1,500 words judging between Kant's Groundwork, Preface and Section 1, and Aristotle on whether a good action is one done from duty or from character, using passages you can reopen. You pass when your listener can state your three points and the objection you answered, and each claim in the essay names a passage in one of the two texts.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Geometry Logic

Seminar

• Immanuel Kant, Groundwork of the Metaphysics of Morals: Section 2

Tutorial: Laboratory

Huygens: double refraction. Read the later chapters, selections, and if you have a clear calcite crystal, look through it at one mark on paper and record how many images you see and where they fall.

• Christiaan Huygens, Treatise on Light: the later chapters, selections

Acts

Check it against evidence, Examine the reasons

Pass when: Look through a clear calcite crystal, or work from the diagrams in the selections if you have none, and record how many images of one mark appear and where. Then write about 1,500 words judging between Kant's Groundwork, Section 2, and Huygens on whether one fact of experience can be explained by a principle that every case must obey, using passages you can reopen. You pass when your record counts the images and places them, and each claim in the essay names a passage or your record.

On the site: Hypotheses, Predictions and Tests

Astronomy Geometry

Seminar

• Immanuel Kant, Groundwork of the Metaphysics of Morals: Section 3

Tutorial: Mathematics

Newton: central forces and the area law. Read the selections on central forces, then for a body moving round a centre, compute the area swept in two equal times at two positions you choose, and show the areas are equal.

• Newton, Principia: Book 1, Sections 2-3, selections

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the area swept by a line from a centre to a moving body in two equal times, at two positions you choose, and show that the two areas are equal under a central force. Then write about 1,500 words judging between Kant's Groundwork, Section 3, and Newton on whether a law of nature can be known by reason alone, using passages you can reopen. You pass when your two areas agree within your error and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Logic

Seminar

• American founding documents, Declaration of Independence: a second reading, in its setting

Tutorial: Language

French: Molière's comedy. Read Acts 1 to 3 of Le Misanthrope or Tartuffe aloud in French, then write one English line for each scene naming who wants what from whom.

• Molière, Le Misanthrope or Tartuffe: Le Misanthrope or Tartuffe, Acts 1-3

Acts

Understand exactly, Express it truly, Examine the reasons

Pass when: Read Acts 1 to 3 of one Molière comedy, Le Misanthrope or Tartuffe, aloud in French, then write one English line for each scene naming who wants what from whom. Then write about 1,500 words judging between the Declaration of Independence, read in its setting, and Hobbes on whether a people may withdraw from its government, using passages you can reopen. You pass when a listener can follow your lines and each claim in the essay names a passage in one of the two texts.

On the site: How to Read a Great Book: Levels, Modes and the Completion Standard

Geometry Logic

Seminar

• American founding documents, Articles of Confederation: the whole text

Tutorial: Mathematics

Newton: the inverse-square law and the conic orbits. Read the selections on the inverse-square law and the conic orbits, then compute the distance from the centre at three points of an orbit with stated eccentricity and semi-latus rectum, and check each by the conic's equation.

• Newton, Principia: Book 1, Sections 2-3, further selections

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the distance from the centre at three angles of a conic orbit with stated eccentricity and semi-latus rectum, and check each answer against the conic's equation. Then write about 1,500 words judging between the Articles of Confederation and Hobbes on whether a union of states can keep the peace without a common power, using passages you can reopen. You pass when your three distances satisfy the equation and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Music Rhetoric

Seminar

• American founding documents, Constitution of the United States: the Constitution and the Bill of Rights

Tutorial: Music

Schubert: songs, the words and the music. Choose three selected songs, read each poem through twice, then listen while following the words, and mark where the music changes with a word or image.

• Schubert, Selected songs: selected songs

Acts

Understand exactly, Express it truly, Examine the reasons

Pass when: Read three selected Schubert songs' poems twice, then listen to each while following the words, and mark where the music changes, with a word or image from the poem. Then write about 1,500 words judging between the Constitution and Bill of Rights and Locke's Second Treatise on whether written limits can protect a people from its own government, using passages you can reopen. You pass when your marks match the songs on a second listening and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Arithmetic Logic

Seminar

• Alexander Hamilton, James Madison and John Jay, Selected Federalist Papers: selected papers, including No. 10

Tutorial: Laboratory

Young: interference. Read the selections on interference, then use a light source and a card with two narrow slits, or the diagrams in the selections if you have no slits, and describe the bands you see. Never look directly into a laser beam.

• Thomas Young, Selected writings: selections

Acts

Check it against evidence, Examine the reasons

Pass when: Set up two narrow slits and a light source, or work from the diagrams in the selections if you have no slits, and describe the bands you see in a table of the spacing you measure. Then write about 1,500 words judging between The Federalist, No. 10, and Plato's Republic on whether a large and varied republic can keep factions from dividing it, using passages you can reopen. You pass when your spacing measurements repeat within your error and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Astronomy Arithmetic

Seminar

• Alexander Hamilton, James Madison and John Jay, Selected Federalist Papers: selected papers, including Nos. 39 and 47-51

Tutorial: Mathematics

Newton: the attraction of spheres, selected propositions. Read the propositions on the attraction of spheres, then compute the force between two spheres at a distance you choose, treating each sphere's mass as concentrated at its centre, and state why that is allowed.

• Newton, Principia: Book 1, further selected propositions

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the force between two spheres at a distance you choose, treating each mass as concentrated at its centre, and state in one paragraph why that treatment is allowed. Then write about 1,500 words judging between The Federalist, Nos. 39 and 47-51, and Hobbes on whether a government can be divided into parts without losing its power, using passages you can reopen. You pass when your calculation uses the stated masses and distances consistently and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Rhetoric

Seminar

• Alexander Hamilton, James Madison and John Jay, Selected Federalist Papers: selected papers, including Nos. 70 and 78

Tutorial: Language

French: Molière's ending. Read Acts 4 and 5 of the same Molière play aloud in French, then write the ending in one English paragraph, naming the last decision of each main character.

• Molière, Le Misanthrope or Tartuffe: Le Misanthrope or Tartuffe, Acts 4-5

Acts

Understand exactly, Express it truly

Pass when: Read Acts 4 and 5 of the Molière play you began aloud in French, then write the ending in one English paragraph naming the last decision of each main character. Then write about 1,500 words judging between The Federalist, Nos. 70 and 78, and Plato's Republic on whether a single executive is safer than a council, using passages you can reopen. You pass when a listener can follow the ending from your paragraph and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Astronomy Logic

Seminar

• Alexis de Tocqueville, Democracy in America: Volume 1, Part 1, selections

Tutorial: Mathematics

Newton: the System of the World begins. Read the rules of reasoning in Book 3, then write each rule in your own words with one example from the motions of the planets and the moon.

• Newton, Principia: Book 3, the Rules of Reasoning and the Phenomena

Acts

Understand exactly, Examine the reasons

Pass when: Write each rule of reasoning from Book 3 of the Principia in your own words, with one example from the motions of the planets. Then write about 1,500 words judging between Tocqueville's Democracy in America, Volume 1, Part 1, selections, and Newton on whether a rule taken from observation can govern a society, using passages you can reopen. You pass when each rule has an example you can state and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Music

Seminar

• Alexis de Tocqueville, Democracy in America: Volume 1, Part 2, selections

Tutorial: Language

French: rhythm and sound, the alexandrine read aloud. Read a passage of Racine's verse aloud, beating the rhythm with your hand, and mark the caesura in each twelve-syllable line.

Acts

Understand exactly, Express it truly

Pass when: Read a passage of Racine's verse aloud, marking the rhythm and the caesura in each twelve-syllable line, and beat the rhythm with your hand while you read. Then write about 1,500 words judging between Tocqueville's Democracy in America, Volume 1, Part 2, selections, and Locke on whether a people's habits can secure its liberty, using passages you can reopen. You pass when a listener can hear the rhythm you marked and each claim in the essay names a passage in one of the two texts.

On the site: Choosing a Language to Study for Reading: Latin, Greek, French, German and Beyond

Arithmetic Logic

Seminar

• Alexis de Tocqueville, Democracy in America: Volume 2, Parts 1-2, selections

Tutorial: Laboratory

Young: the colours of thin plates. Read the further selections on thin plates, then look at a soap film or a thin film of oil on water in daylight, and record the colours in order of thickness.

• Thomas Young, Selected writings: further selections

Acts

Check it against evidence, Examine the reasons

Pass when: Look at a soap film or a thin film of oil on water in daylight, and record the colours in order from the thinnest part to the thickest. Then write about 1,500 words judging between Tocqueville's Democracy in America, Volume 2, Parts 1-2, selections, and Bacon on whether a pattern seen in a small case can show the law of a whole, using passages you can reopen. You pass when your record orders the colours the same way on a second look and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Astronomy Arithmetic

Seminar

• Alexis de Tocqueville, Democracy in America: Volume 2, Parts 3-4, selections

Tutorial: Mathematics

Newton: universal gravitation argued. Read the selections, then compute the force of gravity between two bodies of stated masses at a stated distance, and show how the force changes if the distance doubles.

• Newton, Principia: Book 3, selections

Acts

Understand exactly, Check it against evidence, Examine the reasons

Pass when: Compute the gravitational force between two bodies of stated masses at a stated distance, then show how the force changes when the distance doubles. Then write about 1,500 words judging between Tocqueville's Democracy in America, Volume 2, Parts 3-4, selections, and Plato's Republic on whether a free society tends toward one kind of opinion, using passages you can reopen. You pass when your ratio after doubling matches the inverse-square rule you wrote and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Logic Arithmetic

Seminar

• Jane Austen, Pride and Prejudice: Volume 1

Tutorial: Evidence and inquiry

A causal question answered with public data: what can and cannot be concluded. Choose a question about a cause and an effect that a public table can speak to, state what the table shows, and state what it cannot show.

Acts

Examine the reasons, Check it against evidence, Act and review

Pass when: Choose a question about a cause and an effect that a public table can speak to, then list what the table shows and what it cannot show. Then write about 1,500 words judging between Austen's Pride and Prejudice, Volume 1, and Aristotle on whether a first judgment of another person can be trusted, using passages you can reopen. You pass when both lists give a reason for each entry, your essay names a passage for each claim, and you state how the answer would change if the table were wrong.

On the site: Judgment Under Uncertainty: Probability, Causation and Forecasting

Astronomy Logic

Seminar

• Jane Austen, Pride and Prejudice: Volumes 2-3

Tutorial: Mathematics

Newton: the General Scholium. Read the General Scholium, then write a short account, in your own words, of what Newton says he does not feign and what he claims the phenomena show.

• Newton, Principia: the General Scholium

Acts

Understand exactly, Examine the reasons

Pass when: Write a short account, in your own words, of what the General Scholium says Newton does not feign and what he claims the phenomena show. Then write about 1,500 words judging between Austen's Pride and Prejudice, Volumes 2-3, and Newton on whether a conclusion can be trusted when its cause is not yet known, using passages you can reopen. You pass when your account matches the Scholium when you reopen it and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Grammar Rhetoric

Seminar

• Jane Austen, Emma: Volume 1

Tutorial: Language

French and English expression compared: literal meaning against rhetorical effect. Translate three passages from a French prose selection into English, then write beside each a note on what the English gains or loses in effect.

Acts

Understand exactly, Express it truly

Pass when: Translate three passages from a French prose selection into English, and write beside each a note on what the English gains or loses in effect. Then write about 1,500 words judging between Austen's Emma, Volume 1, and Shakespeare on whether a speaker's literal words or their tone should guide what a listener believes, using passages you can reopen. You pass when a second reader can check each translation against the French and each claim in the essay names a passage in one of the two texts.

On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech

Rhetoric Logic

Seminar

• Jane Austen, Emma: Volumes 2-3

Tutorial: Writing and speaking

Writing: revise one essay for syntax, structure and style. Take an essay you wrote in an earlier level, cut each sentence that repeats a claim, reorder the paragraphs by argument, and rewrite the first and last sentences.

Acts

Express it truly, Examine the reasons

Pass when: Take an essay you wrote in an earlier level, cut each sentence that repeats a claim, reorder its paragraphs by argument, and rewrite its first and last sentences. Then write about 1,500 words judging between Austen's Emma, Volumes 2-3, and Plato's dialogues on whether a clever speaker can mislead a listener through order and wit, using passages you can reopen. You pass when a listener can state the thesis of your revised essay after one reading and each claim in the new essay names a passage in one of the two texts.

On the site: English Expression Mastery: Words, Sentences, Paragraphs and Speech

Arithmetic Logic

Seminar

• Johann Wolfgang von Goethe, Faust: Part 1, to the pact

Tutorial: Laboratory

Interference at home: a double slit lit by a laser pointer, measured (never look into the beam). Make two narrow slits in card, shine a laser pointer through them onto a wall at a measured distance, and measure the spacing of the bands with a ruler.

Acts

Check it against evidence, Examine the reasons

Pass when: Make two narrow slits in card, shine a laser pointer through them onto a wall at a measured distance, and measure the spacing of the bands with a ruler, never looking into the beam. Then write about 1,500 words judging between Goethe's Faust, Part 1, to the pact, and Plato on whether knowledge can be bought at any cost, using passages you can reopen. You pass when your band spacing repeats within your error and each claim in the essay names a passage in one of the two texts.

On the site: Hypotheses, Predictions and Tests

Astronomy Arithmetic

Seminar

• Johann Wolfgang von Goethe, Faust: Part 1, the rest

Tutorial: Mathematics

Kepler's laws derived from Newton's, by hand. Take Newton's inverse-square law for a circular orbit and derive by hand the relation between the square of the period and the cube of the radius, writing each step.

Acts

Understand exactly, Check it against evidence

Pass when: Derive by hand, from an inverse-square force on a circular orbit, the relation between the square of the period and the cube of the radius, writing each step. Then write about 1,500 words judging between Goethe's Faust, Part 1, the rest, and Bacon on whether the study of nature can be a path to power, using passages you can reopen. You pass when each step of your derivation follows from the one before and each claim in the essay names a passage in one of the two texts.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler

Music Rhetoric

Seminar

• Johann Wolfgang von Goethe, Faust: Part 2, selections

Tutorial: Music

Schubert: the argument of a song cycle. Read the words of a song cycle in order, then write its argument in five sentences, and listen to the cycle while following the words.

• Schubert, Selected songs: further songs

Acts

Understand exactly, Express it truly

Pass when: Read the words of a Schubert song cycle in order, write its argument in five sentences, and listen to the cycle while following the words. Then write about 1,500 words judging between Goethe's Faust, Part 2, selections, and Plato on whether a whole life can be shown as a single argument, using passages you can reopen. You pass when your five sentences match the words in order and each claim in the essay names a passage in one of the two texts.

On the site: The Science of Music: Ratios, Beats, the Comma and String Physics

Logic Rhetoric

Seminar

Task: The third-year essay: choose a question on which two modern authors judge differently

Tutorial: Language

English poetry: seventeenth-century poems, a second look at metre and argument. Read five seventeenth-century English poems aloud, mark the metre of each, and write one line on how each poem's argument moves.

Acts

Examine the reasons, Express it truly

Pass when: Choose a question on which two modern authors judge differently, state it in one sentence, and write a 300-word statement of the two positions and the evidence each author would need. Read five seventeenth-century English poems aloud (for example by Donne, Marvell, Bradstreet or Wroth), marking the metre and the argument of each. You pass when a reader can state the question and both positions from your statement alone, and your metre marks repeat on a second reading.

Logic Rhetoric

Seminar

Task: The third-year essay: the draft

Tutorial: Mathematics

Oral examination: one demonstration from the Principia. Prepare one proposition from the Principia, set out its steps by hand, and be ready to explain each step aloud to a listener.

Acts

Examine the reasons, Express it truly

Pass when: Write the draft of the third-year essay, about 1,500 words, judging between the two authors you chose, with the evidence for each claim marked. Then set out one proposition from the Principia by hand, step by step, and explain each step aloud. You pass when every claim in your draft carries a marked passage and a listener can follow your proposition step by step without the book.

Arithmetic Logic

Seminar

Task: The third-year essay: a reader's criticism, and your reply

Tutorial: Laboratory

Particle and wave accounts of light compared: what each explains. Write a table with one row for each phenomenon, such as reflection or interference, and mark which account explains it and which needs an extra assumption.

Acts

Examine the reasons, Check it against evidence, Express it truly

Pass when: Give your draft to one reader for criticism, write a reply of about 300 words to each objection, and build a table of light phenomena with one row each, marking which account explains it and which needs an extra assumption. Then revise the draft's weakest claim. You pass when every objection gets a reply that names a passage, and a reader can check each row of your table against the texts.

On the site: Hypotheses, Predictions and Tests

Grammar Rhetoric

Seminar

Task: The third-year essay: the final text

Tutorial: Language

English poetry: a poem learned by heart, recited and explained. Learn one English poem by heart over a week, recite it without the page, then explain in English its argument and its most difficult line.

Acts

Understand exactly, Express it truly

Pass when: Write the final text of the third-year essay, about 1,500 words, with each objection answered. Then learn one English poem by heart, recite it without the page, and explain its argument and its hardest line in English. You pass when the essay answers every objection from your criticism, and a listener can state the poem's argument after your recitation.

Astronomy Logic Rhetoric

Seminar

Task: The third-year examination: the essay defended aloud, then questions across the year

Tutorial: Mathematics

Mathematical principles and physical phenomena: 800 words on what Newton's mathematics claims to show. Write the 800 words without the book, then read them aloud and mark each claim that needs a proof you can give.

Acts

Examine the reasons, Express it truly, Check it against evidence

Pass when: Write 800 words on what Newton's mathematics claims to show, without the book, then read them aloud and mark each claim that needs a proof. Then defend your third-year essay aloud to a listener, and answer the listener's questions on the year's readings. You pass when the listener can name your thesis and each objection you answered, and you can give the proof of every marked claim without the book.

On the site: Models of the Heavens: Ptolemy, Copernicus, Tycho and Kepler