Ideas in Mathematics

UPenn MATH 1700, Fall 2023.
Ideas in Mathematics

Lecture 22: Example neural net: word type classifier

Lecture 21: Language models and neural net summary

Lecture 20: Gradient flows

Lecture 19: Neural nets nuts and bolts

Lecture 18: Markov Models, toy langugage generation

Lecture 17: Perspectives on AI, neural nets and langauge models

Lecture 16: Computing chromatic polyonmials

Lecture 15: Graph isomorphisms and colorings

Lecture 14: Graph theory and platonic solids

Lecture 13: Some language of graph theory

Lecture 12: Introduction to graphs

Lecture 11: Divisibility and Friday the 13th

Lecture 10 (typed):

Lecture 10: More Modular Arithmetic

Lecture 9: Modular arithmetic entertainment

Lecture 8: Primes and arithmetic

Lecture 7: Counting and the natural numbers

Supplemental sources

History of irrational numbers

(book) A History of Pythagoreanism, edited by Carl A. Huffman (see Sixth-, fifth- and fourth-century Pythagoreans Leonid Zhmud, section 3)

Lecture 6: Infinity and argumentation

Lecture 4: Introduction to Sets

Lecture 3: More on number systems and some modern perspectives

Lecture 2: Number systems and the concept of number

Supplemental sources

Number systems and their history

(book) Numerical Notation, A Comparitive History, by Stephen Chrisomalis

(book) Number Words and Number Symbols, A Cultural History of Numbers by Karl Menninger

Color and language

(book) Through the Language Glass, Why the World Looks Different in Other Languages by Guy Deutscher

(book) You can also find interesting discussions in Chapters 1 and 3 of Reading: the Grand Illusion, How and Why People Make Sense of Print by Ken Goodman, Peter H. Fries, and Steven L. Strauss

The philosophy of number systems

YouTube Video by Numberphile: Do numbers EXIST?

Lecture 1: Introductions