Instructor: David A. Meyer
Office hours: AP&M 7256, M 10:00am-11:00am and Tu 11:00am-12:00nn, or by appointment
Lecture: Solis 111, MWF 9:00am-9:50am
TA: Orest Bucicovschi
Office hours: AP&M 6434, MW 3:00pm-4:00pm, or by appointment
Section: CSB 004, Th 7:00pm-7:50pm; section will not meet Th 21 sep 06
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 are copies of it on reserve in the Science and Engineering Library.
There will be weekly homework assignments, due in section on Thursdays. 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 15% to the final grade.
There will be two midterms, in the fourth and eighth weeks of the quarter. The final is scheduled for Wednesday 6 December. Scores on the two midterms and final will contribute 25%, 25% and 35% to the final grade, respectively. There will be no makeup tests.
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30 nov 06 Kirstin Lauter |
Cryptography and expander graphs |
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16 nov 06 Lily Xu |
Introduction to biostatistics |
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9 nov 06 Dan Rogalski |
The projective plane: Or, how to make ends meet |
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2 nov 06 Wee Teck Gan |
To modularity and beyond |
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26 oct 06 Jamie Pommersheim |
Is infinity plus one prime? (Or: Factorization in the omnific integers) |
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23 oct 06 |
recruiters for Los Angeles Unified School District in San Diego; download poster for information |
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19 oct 06 Russell Quong |
Treating data like vodka: hashing, mashing and distributing |
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12 oct 06 Larry Frank |
Mathematical challenges in magnetic resonance imaging |
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10 oct 06 |
registration deadline for the William Lowell Putnam Mathematical Competition; contact Jeff Rabin for information about registration and practice sessions |
| 7 oct 06 | Harvey Mudd College Mathematics Conference on Enumerative Combinatorics |
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5 oct 06 Nitya Kitchloo |
Fun with spaces |
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28 sep 06 David Meyer |
Winning elections with point-set topology |
| 22 sep 06 |
overview of course HWK (due Th 28 sep 06). Chap. 1: 1,4,7,8,11,12,15,18cdf,22,25,28 |
| 25 sep 06 |
§1.1. Propositions |
| 27 sep 06 |
§1.2. Expressions and tautologies |
| 29 sep 06 |
§1.3. Quantifiers HWK (due Th 5 oct 06). Chap. 1: 41,44,48,50,54,58,61,65,69,71,75,76,84,86,90 |
| 2 oct 06 | §1.4. Methods of proof |
| 4 oct 06 | §1.5-1.6. More proofs |
| 6 oct 06 |
§2.1. Sets HWK (due Th 12 oct 06). Chap. 1: 94,95,100,104; Chap. 2: 3,12,16,20,22,23,30,31,36 |
| 9 oct 06 | §2.2. Set operations |
| 11 oct 06 |
§2.3. Indexed families §2.4. Foundations of set theory HWK (due Th 19 oct 06). Chap. 2: 55,63,64,65,70 |
| 13 oct 06 |
review of Chapters 1 & 2 sample midterm |
| 16 oct 06 |
Midterm 1, covering §1.1-1.6 and §2.1-2.3 Test is open textbook. Bring blue books. |
| 18 oct 06 | solving the problems on Midterm 1 |
| 20 oct 06 |
§3.1. First principle of mathematical induction HWK (due Th 26 oct 06). Chap. 3: 1mq,2,7,9,19,20,35,37 |
| 23 oct 06 |
§3.2. Second principle of mathematical induction |
| 25 oct 06 |
§3.2. Least natural number principle |
| 27 oct 06 |
§3.3. Induction HWK (due Th 2 nov 06). Chap. 3: 41,51,61,64,71,75 |
| 30 oct 06 |
§3.3. Recursion |
| 1 nov 06 |
§3.4. Euclidean algorithm HWK (due Th 9 nov 06). Chap. 3: 83,84a,9394,96,98,100,104,105,110,116 |
| 3 nov 06 | no lecture |
| 6 nov 06 |
§3.5. Elementary number theory |
| 8 nov 06 |
§3.5. The Fundamental Theorem of Arithmetic HWK (due Th 16 nov 06). Chap. 4: 1,2,4,12,13,17acd,19,25 |
| 10 nov 06 | Veteran's Day; no lecture |
| 13 nov 06 |
§4.1. Relations §4.2. Graphs |
| 15 nov 06 | section (Orest) |
| 16 nov 06 |
review of Chapters 3 & 4 (David) §3.5. Problem 112 sample midterm |
| 17 nov 06 |
Midterm 2
Test is open textbook. Bring blue books. |
| 20 nov 06 |
solving the problems on Midterm 2 §4.4; Identifications |
| 22 nov 06 |
§4.3. Equivalence relations §4.4. Partitions HWK (due Th 30 nov 06). Chap. 4: 26,27,33,36,45,51,62,64 |
| 24 nov 06 | No lecture; Happy Thanksgiving! |
| 27 nov 06 |
§4.5. Congruence |
| 29 nov 06 |
§4.6. Composition of relations §5.1. Functions Recommended problems. Chap. 4: 68,71,73,75,83,84,86,87,92; Chap. 5: 1ac,2b,4,9,10,13,15 |
| 1 dec 06 |
§5.2. Functions viewed globally Recommended problems. Chap. 5: 17,20,22 |
| 4 dec 06 |
Review session (David) 6-7pm, AP&M 7421 sample final |
| 5 dec 06 |
Review session (David) 6-7pm, AP&M 7421 sample final |
| 6 dec 06 | Final exam, 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). |
| [3] | D. Solow, How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, 4th edition (Hoboken, NJ: Wiley 2005). |