You can see below how quizzes are graded. If you don’t see a topics list you think should be there, refresh the page.

For every quiz

• You should know what historical claims are made by the text and/or your instructor and what evidence is given to support each one. For example, Struik claims that ancient Mesopotamian mathematics was far more developed than Egyptian mathematics ever was. As evidence, he notes that the Mesopotamians' number system was positional; that they could solve linear and quadratic equations in two variables, whereas the Egyptians could solve only linear equations; that they knew the Pythagorean Theorem in full generality, while the Egyptians knew only special cases; and that they could solve compound interest problems.
  • If I were you, I'd write down every claim I found and a brief summary of the evidence for it, if any is given. I'll bet it would make a great study guide for the final as well as for the quizzes.
• Approximate dates of big things. For example, from what century is the Rhind Papyrus? When did Pythagoras live? Was Eudoxus before or after Archimedes? When was the Nine Chapters compiled?
• The names and major accomplishments of the great mathematicians discussed.
  • I'd add these things to my written notes as well.
• You should know what the words in the text mean. If you don't know one, look it up!

Quiz 1

• Tokens

Quiz 2

• What the main sources of our knowledge of Egyptian mathematics are and about when they are from
• What the method of false position is
• All about rope-stretching
• The process of multiplication by doubling used by the Egyptians
• What Pythagorean triples are and how they are related to triangles
• Major points about the Nine Chapters and about when it was from

Quiz 3

• Why Thales is important in the history of mathematics
• What the three big problems of Greek geometry were
• What “incommensurables” are, how they created a philosophical problem in mathematics, and how the Greek mathematicians responded to them
• What Zeno’s paradoxes were, how they created a philosophical problem in mathematics, and how the Greek mathematicians responded to them

Quiz 4

• What areas of mathematics are discussed in Euclid’s Elements
• What Euclid’s own contribution was
• What the Fifth Postulate says
• Be able to describe how Archimedes approximated π
• What Archimedes’ “Method” was
• What kinds of problems Diophantus worked on

Quiz 5

• What Aryabhata I and Brahmagupta worked on and about when they lived
• When and where zero was first used as a number
• What al-Khwarizmi wrote about and about when he lived
• What Omar Khayyam’s major mathematical accomplishment was and about when he lived
• About when the last great flowering of Chinese mathematics before the twentieth century took place

Quiz 6

• What the Liber Abaci was and why it was important
• Nicole Oresme’s work on the harmonic series
• Who solved the general cubic and when
• The contribution of Viète and its importance
• The idea of Napier’s logarithms

Quiz 7

• What Cavalieri’s Principle says and when it was formulated
• What Descartes’ most important contribution to mathematics was and about when he made it
• What Fermat’s most important contributions to mathematics were and about when he made them
• Be able to describe Fermat’s Method of Infinite Descent precisely
• Who developed the first mathematical theory of probability and about when they did it
• Who first really understood mathematical induction and about when
• The statement of the General Binomial Theorem and why Newton needed it for his development of calculus
• The importance of Newton’s Principia

Quiz 8

• Leibniz’ major accomplishments
• What the calculus provides that earlier work hadn’t
• What the terms in Leibniz’ sum and difference series represent
• How Newton and Leibniz used infinitesimals that opened them to criticism
• Why and about when Bombelli looked into complex numbers
• Why the definitions of function given by Euler in 1748 and by Fourier in 1822 were unsatisfactory from our point of view (I will supply the definitions on the quiz)

Quiz 9

• What was wrong with Lagrange’s approach to the foundations of calculus
• What Cauchy’s contribution to the foundations of calculus was and about when he made it
• How Bishop Berkeley’s objections were finally answered
• About when the insolvability of the general quintic was proved
• What “the quintic is not solvable by radicals” means
• What Galois’ contribution to the theory of polynomial equations was (in broad outline)

Quiz 10

• What was Saccheri’s strategy for proving the Parallel Postulate? Why would it have worked?
• What change did Gauss, Bolyai, and Lobachevsky make to the axioms of Euclidean geometry that led to non-Euclidean geometry?
• What does it mean that Euclidean and hyperbolic geometry are “equiconsistent”?
• What is mathematical platonism?
• What result is considered to be the beginning of set theory? What new proof technique was invented to prove it?
• What are the basic ideas of logicism, formalism, and intuitionism?

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How quizzes are graded

Questions (such as word definitions) with very short answers are worth one point, and you can only get 0 or 1. Other questions are worth three points, and are graded as follows.      

0 -	answer missing or miserable
1 -	some elements of the answer present, or I have to guess at what was meant, or the answer is reasonable but does not directly answer the question asked
2 -	most elements, well expressed: a good answer, just not perfect
3 -	essentially perfect