Mat 406 – History of Mathematics – Fall 08

 

Syllabus:

 

Projects/Reports:

1st Project – Report on Philosophy of Mathematics     2nd Project          3rd Project

                   Logicism – Neil, Jamie and Lintrail

                                Formalism – Amanda Kelsey and Yifan

                                Intuitionism – Casie and Brandon

Assignments:

August 27 -  Discussed:  1) number/numeral; 2) different numeration system names; 3) Tally system; and 4) hieroglyphics and its properties.  First project assignments were made.  Homework:  Problem Set 1.2 – 1, 2, 3.

August 29 – Quiz.  Discussed sets of numbers, kinds of numbers, and sources of ancient mathematical information.  Dates of two earliest papyri were given.  Homework:  Find an example of each kind/set of number – newspapers, magazines, Bible, etc. Problem set 1.2 – 4, 11, 12.

September 3 – Took up homework.  Discussed properties of Mayan, Chinese Bamboo, and Babylonian numerals.  Discussed why we have limited knowledge of really early number use by some civilizations.  Homework:  Complete reading Chapter 1, begin reading Chapter 2.  Problem set 1.3 – 4, 6 ,7 ,13 ,14 ,15 a, b.  Reports are due 9-10-08.

September 5 – Discussed Egyptian arithmetic. Homework:  Problem set 2.3 – 1, 2, 6, 11.

September 8 – Discussed splitting algorithm, Fibonacci’s algorithm, Egyptian method of false position, and other problems from the Rhind Papyrus.  Homework:  Problem set 2.3 – 12, 14, 15, 16, 20, 21, 22 and verify the “identity” in the middle of page 49.

September 10 – Reports on philosophies were given.  Homework problems were address.  Discussion began of 2.4.  Homework:   READ 2.4 – Problem set 2.4 – 1 a, b, 2 a, b, 5, 9.  Earliest possible test date is September 24.

September 12 – Discussed the frustum of a square pyramid and Babylonian equations.  Homework:  Verify the decomposition is equivalent to the formula given.  Verify that the Babylonian quadratic formula is equivalent to the one used today.  Section 2-5:  2, 6, 12.

September 15 -  Took up selected homework problems. Discussed the method that Babylonians used to solve a system of quadratic equations.  Discussed the Plimpton 322 Tablet and possibilities.  Homework:  Verify formula for volume of a fustrum comes from the decomposition proposed in class.  Verify that he Babylonian quadratic formula works.  Section 2.5 – 4, 9, and a couple from 13 (student choice)  Section 2.6 – A couple of problems from 1-4. 

September 17 – Discussed early Greek mathematics (quadrivium, trivium, perfect numbers), Thales and began to discuss Pythagoras. Homework:  Construct 3 perpendiculars, problem Set 3.2 - 8 and 11.

September 19 – Students will watch the video about Pythagoreans.

September 22 – Discussed Pythagoreans and their number theory.  Listed the Platonic solids.  Homework:  Section 3.3 1, 4, 5b, 15, read #17.  Test is on Friday, September 26 on Chapter 1 – 3.

September 24 – Discussed: number of vertices, edges and faces of solids, the famous problems of antiquity, referred to Zeno’s Paradoxes, listed three areas of mathematical development.  Homework hints were given.  TEST IS Moved to OCTOBER 1 on Chapters 1-3.  Students should find Padua on a map (where a Platonic solid dating from 500 B.C. was unearthed) and complete the reading of all three chapters and homework previously assigned.

September 26 – Discussed Construction of a “fourth” proportion.  Homework was to construct two lengths given three lengths.  Other discussion was of what the test next week would be like.\

September 29 – Discussed The Museum at Alexandria and began the discussion of Euclid’s Elements.  Read Chapter 3  (as much as possible) by Friday.
October 1 – Test on Chapters 1-3 – Homework:  READ, READ, READ.

October 3 – Discussed Elements  & Euclid. Constructed the geometric and arithmetic mean, discussed construction of a point to divide a segment into 2 segments in the golden ratio.  Homework:  State Euclid’s 5th postulate, construct an equilateral triangle given a side, construct any triangle given the lengths of the sides, construct the geometric mean between two lengths, Section 4.2 – 2, 5, 12  Complete the two constructions on the handout sheet (the one that had the fourth proportion on it.)

October 6 – Returned tests.  Discussed Euclid’s Algebraic Geometry and some of the number theory in the Elements. Homework:  Construct the diagonal of a regular pentagon, given the length of a side, then use both lengths to construct a regular pentagon.  Homework:  Select and Work at least one more problem from 4.3 (1-7), State the Fundamental Theorem of Arithmetic, and in Section 4.3 – 1, 6, 7, 16a, c.

October 8 – Took a homework problem to grade.  Wrote #2 on the board.  Discussed the pentagon construction again. Discussed Eratosthenes’sieve.  Homework:  4.3 8, 20, 24.  Find all primes less than 300 using Eratosthenes sieve.  Tentative test date is October 22.

October 10 – Took up the sieve.  Discussed Archimedes’ work and accomplishments.  Mentioned Erathosthenes’death and the importance of Euclid’s Elements. Homework:  4.5 –#2 and  read to get the two formulas for area using only sides.

October 15 – Returned homework & Sieve.  Discussed commentators.  Homework:  Section 5.3 – Work at least 3 of the first 12 problems (any way you can) ,

13 & 14.

October 17 – Discussed Hypatia and other commentators in Alexandria, then Arab mathematicians and commentators.  Reports listed as ASAP or Chapter 5 must be complete by October 27 or they will be considered late. Casie and Neil will report on Monday.  Homework:  Section 5.3 – 16 and at least two problems from 16-23; Section 5.4 #2 a, d, e – list the rational roots the verify/check using any method; and Section 5.5 – 1 (at least a couple of these).

October 20 – Discussed Chinese contributions to mathematics.  Two reports, Apollonius and the nine point circle.  Test on Wednesday.

October 22 – Test on 4 & 5.  Begin to Read chapter 6.

October 24 – Discussed Chapter 6 – Homework:  6.2 – 1, 2, 3, read 11.  6.3 – 1, 5

October 27 – Reports were given.  Homework:  Read chapter 7 except for 7.4

October 29 – Report on Regiomontanus.  Discussed the “cubic” argument between Cardano and Tartaglia.  Mentioned several men who were “first” to use symbols that are not standard.  Homework:  7.3 – 1 a, b, d, and 3 a, b, c.

October 31 – Discussed symbolic algebra, and Galileo.  Homework:  8.1 1b, 3, 12a, d.

November 3 – Report on Recorde.  Discussed Lucasian and Savilian professorships (Gresham too).  Discussed Napier and began the discussion of logarithms.

Homework:  Find the logarithm of four numbers given in class.

November 5 – Returned graded reports (project 2).  Discussed computation using logarithms.   Homework:  Handout (outside my office).  Project 3 will be posted by tomorrow.  Email me for choices. 

November 7 – Discussed the slide rule, Kepler, and began the Descartes discussion.  Read through 8.2 – TEST ON 6, 7, and 8 through section 2 on November 14.

November 10 – Discussed Descartes works and his rule of signs.  Mentioned the creators of projective geometry.  Homework:  Handout on nature of the roots of polynomial equations.  Section 8.2 – 4, 5, 7. 

November 12 – Discussed Wallis’ contributions after several homework problems were worked.  Test on Friday administered by Dr. Leavelle.

November 14 – Test

November 17 – Discussed Barrow, Newton, Halley.  Homework:  READ CHAPTER 8

November 19 – Discussed the period of time and people from the mid 1600’s to the 1700’s . . . Newton, Hooke, Leibniz, Wren, Halley and their interaction and accomplishment.  Newton’s Method is the homework.  Problem #11 on page 434 and the sheet outside of my office door.

November 21 – Discussed the final mathematicians in Chapter 8. Began the discussion of Probability mathematicians.  Homework:  Find the equation of the line tangent to the four interesting curves on the handout that you received several meetings ago. 

November 24 – Reports on Sophie Germain and Grace Chisholm Young.  Discussed James and John Bernoulli.

December 1 -  Reports on Charlotte Angas Scott and Karl Weierstrass  Discussed sons of the Bernoulli brothers.  Homework:  9.3 – odd problems.  Fourth scheduled for Friday at 12 at the request of students.  Newton through chapter 9.

December 3 – Reports on Sonya Kovalevsky and Bernard Riemann – Answered questions about 9.3 homework, discussed Mersenne primes and how to produce perfect numbers.  Homework 10.1 – 1, 10.

December 5 – Reports by Brandon and Lintrail – Discussed Fermat and Euler assigned #10 from 10.2

December 8 -  Discussed Euler and Gauss. Homework:  READ sections about Euler, Gauss, Diriclet and Jacobi.   Evaluate Euler’s phi function for numbers <21.  Section 10.3 – 9; Section 10.3 – 13 and 15.

December 10 -  Report from Yifan.  Discussion of History of Non-Eulcidean Geomerties.  Homework:  Section 11.

December 15 – EXAM AT 8.