Math 52: Fundamentals of Mathematics
Fall 2011
Course Info:
- Lectures: Monday, Wednesday, Friday, 10:40 a.m. - 11:30 a.m.
- Dates: 29 August 2011 - 8 December 2011
- Room: Rowell 118
- Course Record Number (CRN): 90863
- Instructor: John Voight
- Office: 16 Colchester Ave, Room 207C
- Phone: (802) 656-2271
- E-mail: jvoight@gmail.com
- Office hours: Mondays, 2:30 - 4:30 p.m.; Wednesdays, 9:00 - 10:00 a.m.; or just make an appointment!
- Course Web Page: http://www.cems.uvm.edu/~voight/52/
- Instructor's Web Page: http://www.cems.uvm.edu/~voight/
- Prerequisites: Math 21 (corequisite).
- Required Text: Larry Gerstein, Introduction to Mathematical Structures and Proofs, corrected edition, 1996.
- Grading: Homework will count for 40% of the grade. Class participation and preparedness will count for 10% of the grade. There will be two 50-minute exams that will each count for 10% of the grade and one comprehensive final exam that will count for 30% of the grade.
Syllabus:
[PDF] Syllabus
[PDF] Master Syllabus
Homework:
[PDF] Homework Submission Guidelines
Homework is due on the same day as the row in which it appears. Problem 3.5.2 means in section 3.5, exercise 2.
| Chapter 1: Logic | ||||
| 1 | 29 Aug | (M) | Hurricane Irene | |
| 2 | 31 Aug | (W) | Introduction, 1.1: Statements, Propositions, and Theorems | |
| 3 | 2 Sep | (F) | 1.2: Logical Connectives and Truth Tables | 1.1.1, 1.1.4 |
| 5 Sep | (M) | No class, Labor Day | ||
| 4 | 7 Sep | (W) | 1.3: Conditional Statements | 1.3.1, 1.3.5, Truth table for "not P and (P or Q)" |
| 5 | 9 Sep | (F) | No class | |
| 6 | 12 Sep | (M) | 1.4: Proofs: Structures and Strategies | 1.3.8, 1.3.10(a)(b), 1.3.11(a)(b), 1.3.12, 1.3.18(a)(b)(c) |
| 7 | 14 Sep | (W) | 1.5: Logical Equivalence | 1.4.2, 1.4.4, 1.4.5, 1.4.6 |
| Chapter 2: Sets, an introduction | ||||
| 8 | 16 Sep | (F) | 2.1: Fundamentals | Distributive laws, 1.5.2, 1.5.4, 1.5.7 |
| 9 | 19 Sep | (M) | 2.1, 2.2: Russell's Paradox | 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5 |
| 10 | 21 Sep | (W) | 2.3: Quantifiers | 2.1.6, 2.1.7 |
| 11 | 23 Sep | (F) | 2.4: Set Inclusion | 2.3.1, 2.3.2, 2.3.3, 2.3.5, 2.3.6, 2.3.9 |
| 12 | 26 Sep | (M) | 2.5: Union, Intersection, and Complement | 2.4.1, 2.4.4, 2.4.5, 2.4.7, 2.4.9 |
| 13 | 28 Sep | (W) | 2.7: The Power Set | 2.5.1, 2.5.2, 2.5.7 |
| 14 | 30 Sep | (F) | Review | |
| 15 | 3 Oct | (M) | Exam 1, covering material in 1.1 - 2.5 | |
| Chapter 2: Sets, continued | ||||
| 16 | 5 Oct | (W) | 2.8: Ordered Pairs and Cartesian Products | 2.7.1, 2.7.5, 2.7.8 |
| 17 | 7 Oct | (F) | 2.9: Set Decomposition: Partitions and Relations | 2.8.4, 2.8.5, 2.8.7(b)(c)(g) |
| 18 | 10 Oct | (M) | 2.9 | 2.9.1, 2.9.2, 2.9.3 |
| 19 | 12 Oct | (W) | 2.9 | 2.9.6, 2.9.7, 2.9.15 |
| 20 | 14 Oct | (F) | 2.10: Mathematical Induction and Recursion | 2.9.11, 2.9.17, 2.9.20 |
| 21 | 17 Oct | (M) | 2.10 | 2.10.1, 2.10.3, 2.10.4 |
| Chapter 3: Functions | ||||
| 22 | 19 Oct | (W) | 3.1: Definitions and Examples | 2.10.2, 2.10.7, 2.10.12 |
| 23 | 21 Oct | (F) | 3.2: Surjections, Injections, Bijections, Sequences | 3.1.1, 3.1.2, 3.1.4, 3.1.5, 3.1.6(a)(b)(c)(d) |
| 24 | 24 Oct | (M) | 3.2 | 3.2.1 (just the functions f(x) in 3.1.4), 3.2.3, 3.2.4 |
| 25 | 26 Oct | (W) | 3.3: Composition of Functions | 3.2.9(a), 3.2.14, 3.2.16 |
| 26 | 28 Oct | (F) | Review | 3.3.7, 3.3.8, 3.3.9 |
| 27 | 31 Oct | (M) | 4.1: Cardinality: Fundamental Counting Principles | |
| 28 | 2 Nov | (W) | Exam 2, covering 2.7-3.3 | |
| Chapter 4: Finite and Infinite Sets | ||||
| 29 | 4 Nov | (F) | 4.2: Comparing Sets, Finite or Infinite | 4.1.5, 4.1.7 |
| 30 | 7 Nov | (M) | 4.2 | 4.2.2, 4.2.4, 4.2.5 |
| 31 | 9 Nov | (W) | 5.8: Binomial Coefficients | |
| Chapter 6: Number Theory | ||||
| 32 | 11 Nov | (F) | 6.1: Operations | 5.8.1(a)(b)(c), 5.8.4, 5.8.5, 5.8.8 |
| 33 | 14 Nov | (M) | 6.2: The Integers: Operations and Order | 6.1.3, 6.1.4, 6.1.7, 6.1.13 |
| 34 | 16 Nov | (W) | 6.3: Divisibility | 6.2.3, 6.2.5, 6.2.9 |
| 35 | 18 Nov | (F) | 6.3 | 6.3.4 |
| 21-25 Nov | (M-F) | No class, Thanksgiving Recess | ||
| 36 | 28 Nov | (M) | 6.3 | |
| 37 | 30 Nov | (W) | 6.3 | 6.3.8, 6.3.10(a)(b) (extended Euclidean algorithm) |
| 38 | 2 Dec | (F) | 6.4: Congruence, Divisibility Tests | 6.3.15 |
| 39 | 5 Dec | (M) | 6.5: Introduction to Euler's Function | 6.4.1, 6.4.4, 6.4.12, 6.4.13(a) |
| 40 | 7 Dec | (W) | Review | |
| 12 Dec | (M) | Comprehensive Final Exam, 7:30 a.m.-10:15 a.m. | ||
Exams:
There will be two midterm exams and a comprehensive final exam.
[PDF] Review #1... [PDF] Solutions
[PDF] Exam #1 ... [PDF] Solutions
[PDF] Review #2
[PDF] Exam #2 ... [PDF] Solutions