Spring 2018 -- Math 170: Ideas in Math

General Info

Instructor: Julia Hartmann, DRL 4N38
(215)898-7847, hartmann@math.upenn.edu
Office Hours MF 2.15-3PM
Even though that day is on a Monday schedule by the university calendar, I will not hold office hours on 1/10.
Lecture: MWF 1-2PM, A8
First Lecture is on 1/10.
Teaching Assistants: Jacob Seidman, 1N1, seidj@sas.upenn.edu, and Shané Winner, 4C9, swinner@seas.upenn.edu
(found here)

Course Content

(1) representation of numbers, sets, cardinality, proofs, irrational and prime numbers; (2) graph theory, Platonic solids; (3) modular arithmetic, cryptography, random number generators, symmetry, and groups; other topics depending on time and interest.

Grading Policy

Homework will be assigned most weeks (11 assignments total), the assignments will be posted on Canvas. The due date is posted with each respective assigment. No late homework will be accepted but the lowest score will be dropped.

There will be three noncumulative in-class exams on the following dates:
Your final grade will be determined based on the following:

10 Assignments40 points each
3 Exams200 points each
Total1000 points
There will be a few in-class quizzes for extra credit. These will not be announced in advance. There is no need to study for the quizzes.


Please sign up for Canvas notifications as I will make announcements there.
There is no textbook for the course. It is important that you attend the lecture and take notes. I will also post notes on Canvas.

Preliminary Schedule

All scheduled events other than exams are subject to change.
1 W 1/10 Introduction, representing numbers, sign-value systems, Roman numerals
2 F 1/12 Positional number systems, decimal number system, binary number system, and other bases
3 W 1/17 Mayan and Babylonian number systems
4 F 1/19 Sets, elements, ∈, ∉, ellipses, union, ∪, intersection, ∩, subsets, ⊆, natural numbers, integers
5 M 1/22 Sets, complements, set-builder notation
6 W 1/24 Definitions, size of a set, cardinality, 1-to-1 matchings between sets, Cantor's definition of cardinality
7 F 1/26 Cardinality, countable sets, integers and rationals are countable, the Grand Hilbert Hotel
8 M 1/29 Uncountable sets, proof by contradiction, √ 2 is not rational, real numbers are uncountable
9 W 1/31 √ 13 is not rational, introduction to number theory
10 F 2/2 There are infinitely many primes, finding primes, Fermat primes, Mersenne primes
11 M 2/5 Sieve of Erathosthenes, Fundamental Theorem of Arithmetic, divisibility, Euclid's Lemma
12 W 2/7 Existence of prime factorizations, uniqueness of prime factorizations
13 F 2/9 Review of number systems, sets, cardinality, and prime numbers; FAQ
15 W 2/14 Gauss' formula, proof by induction
16 F 2/16 Introduction to graph theory, graphs, vertex degrees
17 M 2/19 Degree Sum Formula, connected graphs, regular graphs, complete graphs, bipartite graphs, graph isomorphism
18 W 2/21 Examples of isomorphic and nonisomorphic graphs, planar graphs and faces
19 F 2/23 Euler's formula for planar graphs
20 M 2/26
21 W 2/28
22 F 3/2
23 M 3/12
24 W 3/14
25 F 3/16 Review of graph theory
27 W 3/21 Introduction to secure communication, encryption, ciphers, modular arithmetic
28 F 3/23
29 M 3/26
30 W 3/28
31 F 3/30
32 M 4/2
33 W 4/4
34 F 4/6
35 M 4/9
36 W 4/11
37 F 4/13
38 M 4/16
39 W 4/18
40 F 4/20 Review
42 W 4/27 * Special Lecture *