http://sites.math.rutgers.edu/~zeilberg/math437_21.html

Last Update: Dec. 13, 2021

CLASS POLICY,

TEXT:

• Concise History of Mathematics, by Dirk J. Struik (free download).

• Recommended Extra Reading: History of Mathematics, by Luke Hodgkin (free download)

Instructor

OFFICIAL Rutgers email: zeilberg at math dot rutgeres dot edu

E-mail for this class: DrZLinear@gmail.com

Times

• MW 3:00-4:20pm
  [They are all recorded, but attendance is mandatory]

Office Hour

• On-Line: Wed., 4:30-5:20pm, (after the class, same WebEx link as the Wed. class).

• In person: Tue., 3:30-4:30pm, Hill 704.

Final Project

The coordinator/Editor in Chief is Sarah Magno. Each student is expected to write four to five short essays, to be assigned by Ms. Magno (but you are welcome to request), of the participants in the historic Ramanujan Centennial Conference (1987)

Here is the project page

Due Dec. 7, 2021, 8:00pm (each student will give a short presentation during the last two classes, Dec. 8, and Dec. 13. They can share the screen with their essays.)

FOR EACH OF YOUR (USUALLY FIVE) ESSAYS (MAKE SURE THAT YOU HAVE YOUR NAME AS AUTHOR OF THE ESSAY), THAT SHOULD BE A .pdf FILE, SEND IT AS ATTACHMENTS (as FirstLast.pdf (where FirstLast regards the subject of the essay, not its author), e.g. FreemanDyson.pdf, WITH THE FIRST LETTER CAPITALIZED, TO SARAH MAGNO

sm2253@math.rutgers.edu

YOU CAN SEND ONE EMAIL WITH FIVE ATTACHMENTS.

Lectures

• Wed. , Sept 1: Lecture 0 [please stop watching after 46 minutes, I forgot to "stop recording" and am too lazy to edit it]

  1981 article (by Philip Todd and Dr. Z.)     Mind reading trick     maple code to generate these    

  homework 0 (Due Sunday, Sept. 5, 8:00pm)
  Email DrZlinear@gmail.com with Subject: hw0, and attachment hw0FirstLast.pdf)
  Added Sept. 8, 2021: look at the students' nice solutions in directory.

  Here is the getting to know you quiz and here are are the solutions

  Here is the empty attendance quiz for Lecture 0 and here are the solutions to the attendance quiz for Lecture 0 (except for the attendance questions)

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• Mon. , Sept 6: No class (Labor Day)

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• Wed., Sept 8: Lecture 1 (part I)  Lecture 1 (part II) [The first five minutes were not recorded; I forgot to stop recording after minute 38, so stop watching then]

  Egyptian Fractions   Maple code for Egyptian Fractions   Chinese Remainder Theorem   Dr. Z.'s handout.

  homework 1 (Due Sunday, Sept. 12, 8:00pm)
  Added Sept. 13, 2021: look at the students' nice solutions in directory.

  Here is the empty attendance quiz for Lecture 1 and here are the solutions to the attendance quiz for Lecture 1 (except for the attendance questions)

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• Mon., Sept 13: Lecture 2

  wikipedia article on the SATOR (magic!) word square
  

  MagicWordSquare.txt: A Maple package to generate magic word squares.
  first sample output    second sample output

  wikipedia article on Magic Squares, See also Jonathan Dimond's fascinating article.

  homework 2 (Due Sunday, Sept. 19, 8:00pm)
  Added Sept. 20, 2021: look at the students' nice solutions in directory.

  Here is the empty attendance quiz for Lecture 2 and here are the solutions to the attendance quiz for Lecture 1 (except for the attendance questions)

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• Wed., Sept 15: Lecture 3

  Triangular Numbers   Square Numbers   Pentagonal Numbers   Hexagonal Numbers

  Quiz 1 (0n hw0 and hw1)-
  Here are the full solution

  Here is the empty attendance quiz for Lecture 3
  Here is the solutions to the Attendance quiz for lecture 3 (except the attendnace questions)

  homework 3 (Due Sunday, Sept. 19, 8:00pm)
  Added Sept. 20, 2021: look at the students' nice solutions in directory.

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• Mon., Sept 20: Lecture 4

    Zeno   Zeno's paradoxes   Dr. Z.'s infinity-denying opinion.

  homework 4 (Due Sunday, Sept. 26, 8:00pm)
  Added Sept. 27, 2021: look at the students' nice solutions in directory.

  Here is the empty attendance quiz for Lecture 4
  Here is the solutions to the Attendance quiz for lecture 4 (except the attendnace questions)

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• Wed., Sept 22:Lecture 5

  Pythagorean theorem (wiki)    On Pythagorean triples (wiki)

  Real Quiz 2 (0n hw2 and hw3)
  Here are the full solution

  Here is the empty attendance quiz for Lecture 5
  Here are the solutions to the Attendance quiz for lecture 5 (except the attendnace questions)
  The Native Americacn Pythagoras joke

  homework 5 (Due Sunday, Sept. 26, 8:00pm)
  Added Sept. 27, 2021: look at the students' nice solutions in directory.

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• Mon., Sept 27:Lecture 6

  Euclid's Postulates (From Wolfram MathWorld)   Non-Euclidean Geometry (wiki)   Liar's Paradox (wiki)   Axiomatic_system (wiki)   Gödel's Incompleteness Theorem (wiki)   Dr. Z.'s version of Turing's undecidability

  Here is the empty attendance quiz for Lecture 6
  Here are the solutions to the Attendance quiz for lecture 6 (except the attendnace questions)

  homework 6 (Due Sunday, Oct. 3, 8:00pm)
  Added Oct. 4, 2021: look at the students' nice solutions in directory.

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• Wed., Sept 29:Lecture 7

  [I only started recording after about 30 minutes, sorry. The first part was not that important, how to find the greatest common divisor inefficiently. Then we went over the lecture note below. Please study it carefully]

  Real Quiz 3 (0n hw4 and hw5)
  Here are the Solutions to Real Quiz 3

  Euclidean Algorithm

  homework 7 (Due Sunday, Oct. 3, 8:00pm)
  Added Oct. 4, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 7
  Here are the solutions to the Attendance quiz for lecture 7 (except the attendnace questions)

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• Mon., Oct.4: Lecture 8

  Wikipedia article about sqrt(2)      Dr. Z.'s sqrt(2) article   Jet Wimp's beautiful poem proving that the sqrt(2) of irrational

  homework 8 (Due Sunday, Oct. 10, 8:00pm)
  Added Oct. 11, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 8
  Here are the solutions to the Attendance quiz for lecture 8 (except the attendnace questions)

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• Wed., Oct. 6: Lecture 9

  Real Quiz 4 (0n hw6 and hw7)
  Here are the Solutions to Real Quiz 4

  Dr. Z.'s Lecture Notes about continued fractions

  Empty attendance question for Lecture 9
  Here are the solutions to the Attendance quiz for lecture 9 (except the attendnace questions)

  homework 9 (Due Sunday, Oct. 10, 8:00pm)

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• Mon., Oct. 11: Lecture 10

  Wikipedia article about prime numbers   Dr. Z.'s handout about prime numbers I   Dr. Z.'s handout about prime numbers II

  homework 10 (Due Sunday, Oct. 17, 8:00pm)
  Added Oct. 18, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 10
  Here are the solutions to the Attendance quiz for lecture 10 (except the attendnace questions)

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• Wed., Oct. 13: Lecture 11

  Real Quiz 5 (0n hw8 and hw9)
  Here are the Solutions to Real Quiz 5

  homework 11 (Due Sunday, Oct. 17, 8:00pm)
  Added Oct. 18, 2021: look at the students' nice solutions in directory.

  wikipedia article on the quadratic equation   wikipedia article on Cubic function (the part on Cardano's method)   wikipedia article on elementary symmetric polynomials

  Dr. Z.'s insightful essay

  Empty attendance question for Lecture 11
  Here are the solutions to the Attendance quiz for lecture 11 (except the attendnace questions)

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• Mon., Oct. 18: Lecture 12

  wikipedia article on Taylor series   Dr. Z.'s handout on Taylor series (from Calc2)

  homework 12
  Added Oct. 24, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 12
  Here are the solutions to the Attendance quiz for lecture 12 (except the attendnace questions)

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• Wed., Oct. 20: Lecture 13

  Real Quiz 6 (0n hw10 and hw11)
  Here are the Solutions to Real Quiz 6

  Wikipedia articles about Pi and Machin-like formulas

  homework 13 (due Oct. 24, 2021)
  Added Oct. 24, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 13
  Here are the solutions to the Attendance quiz for lecture 13 (except the attendnace questions)

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• Mon. Oct. 25: Review for Exam I

  Empty attendance question for Review Lecture

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• Wed., Oct. 27: EXAM 1

  Exam I
  Here are the solutions to Exam I

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• Mon., Nov. 1: Lecture 14

  wiki article on Permutations

  homework 14 (due Nov. 7, 2021)
  Added Nov. 8, 2021: look at the students' nice solutions in directory.

  Empty attendance question for Lecture 14
  Here are the solutions to the Attendance quiz for lecture 14 (INCLUDING the attendnace questions)

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• Wed, Nov. 3: Lecture 15
  [no quiz today]

  homework 15 (due Nov. 7)
  Added Nov. 8, 2021: look at the students' nice solutions in directory.

  wiki article on the 15 puzzle   1879 article

  Play it On-Line!   wiki article on Groups

  Empty attendance quiz 15
  Here are the solutions to Part II the Attendance quiz for lecture 15

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• Mon. Nov. 8: Lecture 16

  Lagrange's theorem about groups(wiki)

  homework 16 (due Nov. 14)
  Added Nov. 15, 2021: look at the students' nice solutions in directory
  [Note that in Anna Z.'s otherwise perfect solutions, there is a "typo", the number of elements of A₄ is 12, not 15] .

  Empty attendance quiz for Lecture 16
  Here are the solutions the Attendance quiz for lecture 16

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• Wed. Nov. 10: Lecture 17

  Real Quiz 7 (on homework 14 and 15)
  Here are the Solutions to Real Quiz 7

  wikipedia article on Eulerian paths   Seven Bridges of Könisberg

  homework 17 (due Nov. 14)
  Added Nov. 15, 2021: look at the students' nice solutions in directory

  Empty attendance quiz for Lecture 17
  Former student's solution to Part II of attendance quiz for Lecture 17

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• Mon. Nov. 15: Lecture 18

  wikipedia article on Planar graphs   wikipedia article on Platonic Solids

  Empty attendance quiz for Lecture 18
  Solution to Part II of the attendance quiz for Lecture 18

  homework 18 (due Nov. 21)
  Added Nov. 22, 2021: look at the students' nice solutions in directory

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• Wed. Nov. 17: Lecture 19

  Real Quiz 8 (on homework 16 and 17)
  Solutions to Real Quiz 8

  wiki article on Pascal's Triangle   wiki article on the Binomial Distribution  

  Empty attendance quiz for Lecture 19
  Solution to Part II of the attendance quiz for Lecture 19

  homework 19 (due Nov. 21)
  Added Nov. 22, 2021: look at the students' nice solutions in directory

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• Mon. Nov. 22: Lecture 20

  wiki article on Chaos Theory   wiki article on Fractals   wiki article on the Feigenbaum constant 

  homework 20 (due Nov. 28)
  Added Dec. 5, 2021: look at the students' nice solutions in directory

  Empty attendance quiz for Lecture 20
  Solutions to part II of attendance quiz for Lecture 20

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• Wed., Nov. 24: No class due to Thanksgiving recess

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• Mon. Nov. 29: Lecture 21

  The Riemann Hypothesis (wiki)     The Collatz problem (wiki)     NP-hardness (wiki)

      The Goldbach conjecture (wiki)     twin primes (wiki)

  homework 21 (due Dec. 5)
  Added Dec. 5, 2021: look at the students' nice solutions in directory

  Real Quiz 9 (on homework 18 and 19)
  Solutions to Real Quiz 9

  Empty attendance quiz for Lecture 21
  Solutions to part II of attendance quiz for Lecture 21

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• Wed., Dec. 1: Review for Exam 2

  Empty attendance quiz for Review class for Lecture 2

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• Mon., Dec. 6: Exam 2

  Full solutions to Exam 2

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• Wed., Dec. 8: Students' oral presentations, Part I

  ballot (MANDATORY TO SUBMIT, DUE Tue., Dec. 14, 2021, 10:00am)

  schedule

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• Mon., Dec. 13: Students' oral presentations, Part II

  ballot (MANDATORY TO SUBMIT, DUE Tue., Dec. 14, 2021, 10:00am)

  schedule

Winners of the Best Presentation Contest (by popular vote)

• First Prize: Vivian Choong (average 9.5 out of 10)
• Second Prize: Quinn Buob (average 9.3 out of 10)
• Third Prize: Tied between Nina Chalgeri, Nabhanya Neb, and Abdul-Ahad Butt (each average 9.1 out of 10)

In addition, Dr. Z. decided to award Daniel Rogers a Pi T-shirt for this remarkable essay on Freeman Dyson