Instructor: David A. Meyer
Office hours: AP&M 7256, T 12:30-1:30 and F 12:00-1:00, or by appointment
Lecture: WLH 2207, MWF 11:00-11:50
TA: Tai Melcher
Office hours: AP&M 6402E, W 2:00-3:30, Th 12:30-2:00, or by appointment
Section A01: Center 205, F 4:00-4:50
Section A02: Center 205, F 5:00-5:50
This course is an introduction to mathematical reasoning. For anyone, perhaps the most useful consequence of studying mathematics is an enhanced ability to analyze problems, mathematical or otherwise, logically. In advanced mathematics courses, and in mathematics research, this ability is deployed primarily to prove that specific statements are true. The goal of this course is for the students to learn what it is to do mathematics, beyond simply doing calculations. This includes learning what kinds of statements need proof, what constitutes a proof, and how to read and write proofs.
The prerequisite for this course is 20F, or the consent of the instructor. The textbook is P. Fletcher and C. W. Patty, Foundations of Higher Mathematics, 3rd ed., (Pacific Grove, CA: Brooks/Cole Publishing Co. 1996).
There will be weekly homework assignments, due in section on Fridays. Please follow the formatting guidelines. Students are allowed to discuss the homework among themselves, but are expected to turn in their own work — copying someone else's is not acceptable. Homework scores will contribute 20% to the final grade.
There will be two midterms, on Friday 17 October and Wednesday 12 November. The final is scheduled for Wednesday 10 December. The two midterms and final will contribute 20%, 25% and 35% to the final grade, respectively. There will be no makeup tests.
|
winter 04 David A. Meyer |
MATH 111A: Introduction to Mathematical Modelling |
| 15 feb 04 | application deadline for RIPS-2004 |
|
10 dec 03 Kristin Lauter |
RSA cryptography |
|
3 dec 03 David A. Meyer |
Coloring, quantum mechanics, and Euclid |
| 25 nov 03 |
Fall Career Seminar for Math Majors 3:30pm AP&M 2402 |
|
13 nov 03 John de Pillis |
discussion/signing of 777 Mathematical Conversation Starters |
|
12 nov 03 John Eggers |
An elementary introduction to juggling and juggling mathematics |
|
6 nov 03 David Brin |
discussion/signing of The Life Eaters |
|
5 nov 03 Peter Ebenfelt |
The classical Dirichlet problem with rational data |
|
27 oct 03 Kristin Lauter |
RSA cryptography Postponed due to fires. |
|
22 oct 03 Fan Chung Graham |
The mathematics of Internet graphs |
|
17 oct 03 Patrick Fitzsimmons |
Putnam Competition registration; practice begins |
| 26 sep 03 |
overview of course §1.1. Propositions no sections today HWK (due F 3 oct 03). Chap. 1: 1,4,7,8,11,12,15,18cdf,22,25,28 |
| 29 sep 03 | §1.2. Expressions and tautologies |
| 1 oct 03 |
§1.3. Quantifiers |
| 3 oct 03 |
§1.4-1.5. Proof types HWK (due F 10 oct 03). Chap. 1: 41,44,48,50,54,58,61,65,69,71,75,76,84,86,90 |
| 6 oct 03 |
§1.5-1.6. Proofs |
| 8 oct 03 |
§2.1. Sets (Tai) |
| 10 oct 03 |
§2.2. Set operations (Tai) HWK (due F 17 oct 03). Chap. 1: 94,95,100,104; Chap. 2: 3,12,16,20,22,23,30,31,36 |
| 13 oct 03 | §2.3. Indexed families |
| 15 oct 03 | review |
| 17 oct 03 | Midterm 1, covering §1.1-1.6 and §2.1-2.3 Test is open textbook. Bring blue books. HWK (due F 24 oct 03). Chap. 2: 55,63,64,65,70 |
| 20 oct 03 | §3.1. First Principle of Mathematical Induction |
| 22 oct 03 | §3.2. Second Principle of Mathematical Induction |
| 24 oct 03 | §3.2. Least Natural Number Principle HWK (due F 31 oct 03). Chap. 3: 1mq,2,7,9,19,20,35,37 The due date for the problems from §3.3 is postponed to 7 nov 03. |
| 27 oct 03 | All UCSD classes cancelled due to fire. |
| 29 oct 03 | All UCSD classes cancelled due to fire. |
| 31 oct 03 | §3.3. Recursion HWK (due F 7 nov 03). Chap. 3: 41,51,61,64,71,75,83,84a,93 |
| 3 nov 03 | §3.4. Euclidean algorithm |
| 5 nov 03 | §3.5. Diophantine equations |
| 7 nov 03 |
§3.5. Elementary number theory HWK (due F 14 nov 03). Chap. 3: 94,96,98,100,104,105,110,116 |
| 10 nov 03 |
§3.5. Fundamental theorem of arithmetic review sessions: WLH 2207, 12-1:20; AP&M 6438, 6-7:30 |
| 12 nov 03 | Midterm 2, covering §3.1-3.5. Test is open textbook. Bring blue books. |
| 14 nov 03 |
§4.1. Relations and graphs (Tai) HWK (due F 21 nov 03). Chap. 4: 1,2,4,12,13,17acd,19,25 |
| 17 nov 03 | §4.2: Graphs and directed graphs |
| 19 nov 03 | Lecture cancelled; sorry. |
| 21 nov 03 | §4.3-4.4. Equivalence relations and classes |
| 24 nov 03 |
§4.5. Congruence HWK (due M 1 dec 03). Chap. 4: 26,27,33,36,45,51,62,64 |
| 26 nov 03 | No lecture; Happy Thanksgiving! |
| 28 nov 03 | UCSD holiday; Happy Thanksgiving! |
| 1 dec 03 |
§5.1, 5.2. Functions as relations Recommended problems. Chap. 4: 68,71,73,75,83,84; Chap. 5: 1ac,2b,4,9,10,13,15 |
| 3 dec 03 | §9.1. Convergence of sequences |
| 5 dec 03 | §9.2. Sequences Recommended problems. Chap. 9: 2,6,10,12,19,26,27,28,34 |
| 7 dec 03 | Review session 5-7pm, H&SS 1330 |
| 8 dec 03 |
office hours: David 11-12; Tai 1-2 Review session 6-8pm, H&SS 1330 |
| 9 dec 03 | office hours: David 11-12; Tai 1-2 |
| 10 dec 03 | Final exam 11:30-2:30, covering the whole course. Test is open textbook. Bring blue books. |
| [1] | D. R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid (New York: Basic Books 1979). |
| [2] | G. Polya, How to Solve It: a New Aspect of Mathematical Method (Princeton, NJ: Princeton University Press 1945). |