Spring 2019 -- 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 1/16.
Lecture: MWF 1-2PM, A8
First Lecture is on 1/16.
Teaching Assistants: Christopher Bailey, 4C19, bailey89@sas.upenn.edu,
Anschel Schaffer-Cohen, 3N2B, anschel@math.upenn.edu, office hrs F 9-11
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Course Content

(1) representation of numbers, sets, cardinality, basic logic, 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.

Expectations

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. I will post notes on Canvas.

Preliminary Schedule

All scheduled events other than exams are subject to change.
1 W 1/16 Introduction, representing numbers, sign-value systems, Roman numerals, place-value systems, decimal numbers
2 F 1/18 Positional number systems, decimal number system, binary number system, hexadecimal system, Mayan and Babylonian number systems
M 1/21 NO CLASS
3 W 1/23 Sets, elements, ∈, ∉, ellipses, union, ∪, intersection, ∩, subsets, ⊆
4 F 1/25 natural numbrs, integers, complements, set-builder notation
5 M 1/28 Definitions, size of a set, cardinality, 1-to-1 matchings between sets, Cantor's definition of cardinality
6 W 1/30 Cardinality, countable sets, integers and rationals are countable, the Grand Hilbert Hotel
7 F 2/1 Introduction to mathematical arguments and logic: statements, negation, conjunction (and), disjunction (or)
8 M 2/4 Quantifiers, proof by contradiction, √ 2 is not rational
9 W 2/6 Uncountability of the real numbers, introduction to Number Theory
10 F 2/8 Prime numbers, there are infinitely many primes, finding primes, Fermat primes, Mersenne primes
11 M 2/11 Sieve of Erathostenes, Fundamental Theorem of Arithmetic, divisibility, Euclid's Lemma
12 W 2/13 Gauss' formula, proof by induction
13 F 2/15 Review
14 M 2/18 FIRST MIDTERM EXAM
15 W 2/20
16 F 2/22
17 M 2/25
18 W 2/27
19 F 3/1
SPRING BREAK
20 M 3/11
21 W 3/13
22 F 3/15
23 M 3/18
24 W 3/20
25 F 3/22
26 M 3/25
27 W 3/27 Review
28 F 3/29 SECOND MIDTERM EXAM
29 M 4/1
30 W 4/3
31 F 4/5
32 M 4/8
33 W 4/10
34 F 4/12
35 M 4/15
36 W 4/17
37 F 4/19
38 M 4/22
39 W 4/24
40 F 4/26
41 M 4/28 Review
42 W 5/1 THIRD MIDTERM EXAM