| 1 |
Jan 12 |
Introduction; Argument and Proof |
1.1 |
- |
- |
HW1 assigned. |
| 2 |
Jan 14 |
An extremal argument; Pythagorean Theorem |
1.1 |
- |
- |
- |
| 3 |
Jan 19 |
More "proofs" of the Pythagorean Theorem |
1.1 |
- |
- |
HW1 due. HW2 assigned. |
| 4 |
Jan 21 |
Primes; definitions; proof by contradiction |
1.1.2 |
- |
- |
- |
| 5 |
Jan 26 |
Irrational numbers |
1.1.3 |
Q1 |
Q1-soln |
- |
| 6 |
Jan 28 |
Irrational numbers; Algebra in mathematical arguments |
1.2.2 |
- |
- |
HW3 assigned. |
| 7 |
Feb 2 |
Language of math: or and implications |
1.2.2-1.2.4 |
Q2 |
Q2-soln |
HW2 due. |
| 8 |
Feb 4 |
Language of math: quantifiers; polynomials |
1.2.4,1.3.3 |
- |
- |
HW3 due. HW4 assigned. |
| 9 |
Feb 9 |
Roots and factors of polyomials |
1.3.3 |
Q3 |
Q3-soln |
- |
| 10 |
Feb 11 |
Quadratic formula |
1.3,3,1.4 |
- |
- |
HW4 due. HW5 assigned. |
| 11 |
Feb 16 |
Abstraction and examples; executing proofs; large gaps between primes |
- |
- |
- |
- |
| 12 |
Feb 18 |
Test 1 |
1 |
T1 |
T1-soln |
HW5 assigned. |
| 13 |
Feb 23 |
The sum 1+2+...+n |
1.4 |
- |
- |
- |
| 14 |
Feb 25 |
Sigma/Pi sum/product notation; application: how many regions are created by n lines? |
1.4,2.2.2 |
- |
- |
HW5 due. HW6 assigned. |
| 15 |
Mar 1 |
Patterns: a cautionary tale; Intro to sets |
3.1 |
Q5 |
Q5-soln |
- |
| 16 |
Mar 3 |
Set operations |
3.5 |
- |
- |
HW6 due. HW7 assigned. |
| 17 |
Mar 8 |
Proofs with sets; Russell's Paradox |
3.3,3.9 |
Q6 |
Q6-soln |
- |
| 18 |
Mar 10 |
Cartesian products; indexed operations |
3.6,3.7 |
- |
- |
HW7 due. HW8 assigned. |
| 19 |
Mar 15 |
Indexed operations; applications (bounds on n!, harmonic series); proofs |
3.9 |
Q7 |
Q7-soln |
- |
| 20 |
Mar 17 |
Mathematical logic: statements |
4.1 |
- |
- |
HW8 due. |
| 21 |
Mar 29 |
Mathematical logic: statements, variable propositions, quantifiers |
4.1-4.3 |
- |
- |
HW9 assigned. |
| 22 |
Mar 31 |
Negation of quantified statements, Logical connectives, implications |
4.4-4.7 |
- |
- |
- |
| 23 |
Apr 5 |
Proofs, sets, and mathematical logic |
4.8-4.10 |
- |
- |
HW9 due. |
| 24 |
Apr 7 |
Test 2 |
- |
T2 |
T2-soln |
- |
| 25 |
Apr 12 |
Review Test 2; Converse and Contrapositive |
4.8 |
- |
- |
HW10 assigned. |
| 26 |
Apr 14 |
Proof techinique: no minimum counter-example |
- |
Q9 |
Q9-soln |
- |
| 27 |
Apr 19 |
A combinatorial game; geometric coloring example |
5 |
- |
- |
HW11 assigned. |
| 28 |
Apr 21 |
Induction and the no minimum counter-example technique |
5 |
- |
- |
- |
| 29 |
Apr 26 |
Induction |
5 |
- |
- |
- |
| 30 |
Apr 28 |
Review Final Exam; Intro to Ramsey Theory |
- |
- |
- |
HW11 due. |
| -- |
May 3 |
Final Exam: 7pm to 9pm |
- |
- |
- |
- |