Mat 5401 – History of Mathematics

 

 

Syllabus:

 

 

Projects/Reports:

          1st Project – Report on Philosophies of Mathematics          2nd 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 – Same as MAT 406.

September 5 – Discussed Egyptian arithmetic. Homework:  Problem set 2.3 – 1, 2, 8, 11.

September 8 – Same as Mat 406.

September 10 – Reports were given.  Discussed section 2.4 – Homework:  Section 2-4 1 a, b, 2 a 5, 9.  Test on Chapters 1 – 3 may be on 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:  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 4.3 – 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.

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.