History of Mathematics (Math 436), Spring 2017 (Rutgers, NB)

(Last Update: April 24, 2017) http://sites.math.rutgers.edu/~zeilberg/math436_17.html

CLASS POLICY
Textbook: Concise History of Mathematics, by Dirk J. Struik (free download).
Recommended Extra Reading: History of Mathematics, by Luke Hodgkin (free download)
Instructor: Dr. Doron Zeilberger (aka as Dr. Z.)
Dr. Z.'s Office Hours: Mondays and Thursdays, 9:10-10:10am, Hill 704.

This class fulfills the writing requirement of Rutgers. An important part of writing is reading. I am not a history professor, and will not cover any of the historical narrative in class. You are expected to read it on your own. One half of each homework assignment consists of summarizing (in one or two pages, in your own words, and own handwriting) each assigned reading portion. During the quizzes and exams, you can look at your notebook (but no books allowed, neither, of course, the internet). The other half of each homework assignment will be to perform an algorithm or proof presented in class. In each class we will decide together what historically (and mathematically) important algorithm or proof to cover, andI will assign homework (about the studied algorithm or proof) in class (and post it on-line after class).

The quizzes and exams will also be half "history" (and you are welcome to consult your hand-written notebook) and one half "real math" (inspired by the history), that will be covered in class. Homework will be assigned, based on what we did in class, each time, the night after each class.

Added Feb. 26, 2017: Decide on a topic for final project.

You are welcome to participate in the on-going Challenge ProblemsContest [totally optional, for fun and glory, and modest prizes, does not influence the grade at all]

To find out magic word-squares with students' name, find your file-name in this directory

For some of the homework you need to print out square-paper .

For the Two Proofs of the Pythagorean Theorem, download the pictures in this directory .

Schedule

Thurs., Jan. 19: Introduction and Diagnostic Test
[Here are the Solutions (and important comments)]
Monday, Jan. 23: Chapter I (pp. 1-11)
1981 article (by Philip Todd and Dr. Z.)
homework 0 (due Feb. 2)
[Added Jan. 23, 2017: Here is the attendance quiz and here are the full solutions.]
Thurs., Jan. 26: Chapter II, sections 1-3 (pp. 13-23) Egyptian Fractions and Chinese Remainder Theorem [Dr. Z.'s handout]
homework 1 (due Feb. 2)
[Added Jan. 26, 2017: Here is the attendance quiz and here are the full solutions.]
Monday, Jan. 30: Chapter II, sections 4-5 (pp. 23-31) Magic Squares. See also Jonathan Dimond's fascinating article.
homework 2 (due Feb. 9)
[Added Jan. 30, 2017: Here is the attendance quiz and here are the full solutions.]
Thurs, Feb. 2: Chapter II, sections 6-8 (pp. 31- 36) Triangular Numbers Square Numbers Pentagonal Numbers Hexagonal Numbers
homework 3 (due Feb. 9)
Quiz 1 (on hw0 and hw1)
[Added Feb. 2, 2017: Here is the real quiz 1 and here are the full solutions of quiz 1]
[Added Feb. 2, 2017: Here is the attendance quiz and here are the full solutions.]
Monday, Feb. 6: Chapter III, sections 1-4 (pp. 39-50) Zeno Zeno's paradoxes Dr. Z.'s infinity-denying opinion.
homework 4 (due Feb. 16)

[Added Feb. 6, 2017: Here is the attendance quiz and here are the full solutions.]
Thurs, Feb. 9: Chapter III, sections 5-7 (pp. 50-61) homework 5 (due Feb. 16) [Quiz 2 (on hw2 and hw3) is postponed to Monday, Feb. 13, 2017]
[CLASS CANCELLED DUE TO SNOW STORM]
Monday, Feb. 13: Chapter III, sections 8-15 (pp. 61-80) homework 6 (due Feb. 23)
Pythagorean theorem(wiki) Many proofs of Pythagoras (from Alexander Bogomolny's wonderful "Cut the Knot" website) Pythagorean Triple(wiki)
Quiz 2 (on hw2, hw3), rescheduled from Feb. 9, 2017.
[Added Feb. 13, 2017: Here is the attendance quiz and here are the full solutions.]

[Added Feb. 13, 2017: Here is the Real Quiz 2 and here are the full solutions of Real Quiz 2 ]
Thurs, Feb. 16: Chapter IV (pp. 83-96) homework 7 (due Feb. 23)
Euclid's Postulates Non-Euclidean Geometry Axiomatic_system Godel's Incompleteness Theorem Liar's Paradox Quiz 3 (on hw4 and hw5)

[Added Feb. 16, 2017: Here is the Real Quiz 3 and here are the full solutions of Real Quiz 3 ]
[Added Feb. 16, 2017: Here is the attendance quiz and here are the full solutions.]
Monday, Feb. 20: Chapter V, sections 1-6 (pp. 98- 109) The Euclidean Algorithm homework 8 (due March 2)
[Added Feb. 20, 2017: Here is the attendance quiz and here are the full solutions.]
Thurs, Feb. 23: Chapter V, sections 7-9 (pp. 109- 121). Wikipedia article about sqrt(2) Dr. Z.'s sqrt(2) article Jet Wimp's beautiful poem proving that the sqrt(2) of irrational
homework 9 (due March 2) Quiz 4 (on hw6 and hw7)
Added Feb. 23, 2017: Here is the real quiz 4 and here are the full solutions to real quiz 4
Added Feb. 23, 2017: Here is the attendance quiz and here are the full solutions.
Monday, Feb. 27: Chapter VI, sections 1-4 (pp. 125-141) Wikipedia article about prime numbers Dr. Z.'s handout about prime numbers I Dr. Z.'s handout about prime numbers II
homework 10 (due March 9)

Added Feb. 27, 2017: Here is the attendance quiz and here are the full solutions.
Thurs, March 2: Chapter VI, sections 5-7 (pp. 141-154) wikipedia article on the quadratic equation wikipedia article on Cubic function (the part on Cardano's method) wikipedia article on elementary symmetric polynomials
homework 11 (due March 9) Quiz 5 (on hw8 and hw9)
Added March 2, 2017: Here is the real quiz 5 and here are the full solutions to real quiz 5
Added March 2, 2017: Here is the attendance quiz and here are the full solutions.
Monday, March 6: Chapter VI, section 8 (pp. 154-160) wikipedia article on Taylor series Dr. Z.'s handout on Taylor series (from Calc2)
homework 12 (due March 23)

Added March 6, 2017: Here is the attendance quiz and here are the full solutions.
Thurs, March 9: Chapter VII, sections 1-4 (pp. 163-175)
All about π
Wikipedia articles about Pi and Machin-like formulas
homework 13 (due March 23)
Quiz 6 (on hw10 and hw11)
Added March 9, 2017: Here is the real quiz 6 and here are the full solutions to real quiz 6
Added March 9, 2017: Here is the attendance quiz and here are the full solutions.
Monday, March 13: Spring Break (No Class)
Thurs, March 16: Spring Break (No Class)
Monday, March 20: REVIEW
Added March 20, 2017: Here is the attendance quiz and here are the full solutions.
Thurs, March 23: Exam I (on hw1-hw13)
Added March 25, 2017: Here is the Exam I and here are the full solutions to Exam I
Monday, March 27: Chapter VII, sections 5-7 (pp. 175- 186) homework 14 (due April 6)
wiki article on Permutations
Added March 25, 2017: Here is the attendance quiz 14 and here are the full solutions
Thurs, March 30: Chapter VII, sections 8-10 (pp. 186-192) homework 15 (due April 6)

wiki article on the 15 puzzle 1879 article
Play it On-Line! wiki article on Groups
Added March 30, 2017: Here is the attendance quiz 15 and here are the full solutions
Monday, April 3: Chapter VII, section 11 (pp. 192-199) homework 16 (due April 13)
wikipedia article on Eulerian paths Seven Bridges of Könisberg
Added April 3, 2017: Here is the attendance quiz 16 and here are Alicia Sukhram's full solutions, and Joshua Pomerantz's full solutions (that also indicates the Eulerian cycle and path, when they exist) [both posted by kind permission]
Thurs, April 6: Chapter VIII, sections 1-3 (pp. 201-209) homework 17 (due April 13) wikipedia article on Planar graphs wikipedia article on Platonic Solids
Quiz 7 (on hw14 and hw15)
Added April 6, 2017: Here is the attendance quiz 17 and here are the solutions

Added April 6, 2017: Here is the real quiz 7 and here are solutionss
Monday, April 10: Chapter VIII, sections 4-6 (pp. 209-219) homework 18 (due April 20)
Catch Up! Detecting Gibberish. More on the 15 puzzle.
Added April 10, 2017: Here is attendance quiz 18 and here are its solutions
Thurs, April 13: Chapter VIII, sections 7-8 (pp. 219-226) homework 19 (due April 20) Quiz 8 (on hw16 and hw17)
wiki article on Pascal's Triangle wiki article on the Binomial Distribution
Added April 13, 2017: Here is attendance quiz 19 and here are its solutions
Added April 13, 2017: Here is Real quiz 8 and here are its Solutions to Quiz 8
Monday, April 17: Chapter VIII, sections 9-12 (pp. 226-232) homework 20 (due April 24 [ Note New due date])
wiki article on Chaos Theory wiki article on Fractals wiki article on the Feigenbaum constant wiki article on the Mandelbrot set
Added April 17, 2017: Here is attendance quiz 20 and here are its solutions
Thurs, April 20: Chapter VIII, sections 13-15 (pp. 233-244) homework 21 (due April 27) (due April 27) [Only reading homework] Quiz 9 (on hw18 and hw19)
REVIEW

Added April 20, 2017: Here is Real Quiz 9 and here are its solutions to Real Quiz 9
Added April 20, 2017: Here is attendance quiz 21 and here are its solutions
Monday, April 24: Exam II (On Everything, with a slight emphasis on the material after Exam I). Homeworks 1-20, but NOT hw21.

Added April 24, 2017: Here is Exam 2 and here are the solutions to Exam 2
Thurs, April 27: Students' presentations of final projects
Monday, May 1: Students' presentations of final projects

Added April 27, 2017: Congratulations to the winners of the Challenge ProblemsContest

Zongzie Deng: 595 points
Lauren Squillace: 397 points
Tyler Volpe : 185 points

They each win a π T-shirt (with many formuals involving π) [Originally the prize was supposed to be the book "How To Solve it" by George Polya, but it is a free download for everyone!]

Congratulations also to the runner-ups:

Poorva Sampat: 87 points
Suiliang Ma: 60 points
Cassandra Sanchez: 50 points

Added May 1, 2017: The winners of the peer-reviewed oral presentations are (the averages out of 10)

Joshua Pomerantz, 8.958333333
Karine Yamout, 8.780000000
Kevin Lin, 8.592592593

Added May 4, 2017: Read the students' fascinating essays

Doron Zeilberger's teaching page