Math 52: Fundamentals of Mathematics
Fall 2012
Course Info:
- Lectures: Monday, Wednesday, Friday, 9:35 a.m. - 10:25 a.m.
- Dates: 27 August 2011 - 5 December 2011
- Room: Perkins 107
- Instructor: John Voight
- Office: 16 Colchester Ave, Room 207C
- Phone: (802) 656-2271
- E-mail: jvoight@gmail.com
- Office hours: Mondays and Wednesdays, 2:00 - 3:30 p.m.; or just make an appointment!
- Course Web Page: http://www.cems.uvm.edu/~jvoight/52/
- Instructor's Web Page: http://www.cems.uvm.edu/~jvoight/
- Prerequisites: Math 21 (corequisite).
- Required Text: Gary Chartrand, Albert Polimeni, and Ping Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 2nd edition, 2007.
- Grading: Daily readiness homework will count for 10% of the grade. Weekly homework will count for 40% of the grade. Class participation and preparedness will count for 5% 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 25% of the grade.
Syllabus:
[PDF] Syllabus
Homework:
[PDF] Homework Submission Guidelines
Homework is due on the same day as the row in which it appears.
| Chapter 1: Sets | Daily | Weekly | |||
| 1 | 27 Aug | (M) | Introduction | ||
| 2 | 29 Aug | (W) | 0, 1.1 | Read Chapter 0 | |
| 3 | 31 Aug | (F) | 1.2, 1.3 | 1.1, 1.4 | |
| 3 Sep | (M) | No class, Labor Day | |||
| 4 | 5 Sep | (W) | 1.4 | 1.9, 1.10, 1.17 | |
| 5 | 7 Sep | (F) | 1.5, 1.6 | 1.27 | 1.3, 1.6, 1.8, 1.12, 1.18 |
| Chapter 2: Logic | Daily | Weekly | |||
| 6 | 10 Sep | (M) | 2.1, 2.2 | 1.32, 1.41 | |
| 7 | 12 Sep | (W) | 2.3, 2.4, 2.5 | 2.1, 2.2, 2.8 | |
| 8 | 14 Sep | (F) | 2.6, 2.7 | 2.14, 2.15 | 1.26, 1.33, 1.38, 1.43, 1.52 |
| 9 | 17 Sep | (M) | 2.8, 2.9 | 2.23, 2.30 | |
| 10 | 19 Sep | (W) | 2.10 | 2.34, 2.39 | |
| 11 | 21 Sep | (F) | 2.10, 2.11 | 2.43 | 2.4, 2.7, 2.12, 2.18, 2.36 |
| 12 | 24 Sep | (M) | Exam 1, covering material in 1.1-2.9 | ||
| Chapter 3: Direct Proof and Proof by Contrapositive | Daily | Weekly | |||
| 13 | 26 Sep | (W) | 0, 3.1 video | Reread Chapter 0 | |
| 14 | 28 Sep | (F) | 3.2 | 3.1 | 2.46, 2.48, 2.49 |
| 15 | 1 Oct | (M) | 3.3 | 3.6, 3.10 | |
| 16 | 3 Oct | (W) | 3.4, 3.5 | 3.13 (use contrapositive), 3.17 | |
| Chapter 4: More on Direct Proof and Proof by Contrapositive | Daily | Weekly | |||
| 17 | 5 Oct | (F) | 4.1 | 3.19 | 3.5, 3.18, 3.31 |
| 18 | 8 Oct | (M) | 4.2 | 4.2 | |
| 19 | 10 Oct | (W) | 4.3 | 4.11 | |
| 20 | 12 Oct | (F) | 4.4, 4.5 | 4.20 | 3.20, 3.25, 3.27, 3.28, 4.3, 4.10 |
| Chapter 5: Existence and Proof by Contradiction | Daily | Weekly | |||
| 21 | 15 Oct | (M) | 5.1 | 4.33, 4.34 | |
| 22 | 17 Oct | (W) | 5.2 | 5.5 | |
| Chapter 6: Mathematical Induction | Daily | Weekly | |||
| 23 | 19 Oct | (F) | 6.1 | 5.11 | 4.12, 4.17, 4.24, 4.30 |
| 24 | 22 Oct | (M) | 6.2 | 6.5 | |
| Chapter 8: Equivalence Relations | Daily | Weekly | |||
| 25 | 24 Oct | (W) | 8.1, 8.2 | 6.17 | |
| 26 | 26 Oct | (F) | 8.3 | 8.5 | 5.3, 5.16, 5.21, 6.4, 6.14, 6.18 |
| 27 | 29 Oct | (M) | Review | 8.16 | |
| 28 | 31 Oct | (W) | Exam 2, covering 2.10-6.2 | ||
| 29 | 2 Nov | (F) | 8.4 | 8.6, 8.9, 8.17, 8.18 | |
| 30 | 5 Nov | (M) | 8.5, 8.6 | 8.24 | |
| Chapter 9: Functions | Daily | Weekly | |||
| 31 | 7 Nov | (W) | 9.1 | 8.37 | |
| 32 | 9 Nov | (F) | 9.3 | 9.2 | 8.28, 8.30, 8.39, 8.46 |
| 33 | 12 Nov | (M) | 9.4 | 9.11 | |
| 34 | 14 Nov | (W) | 9.5 | 9.20 | |
| 35 | 16 Nov | (F) | 9.5 | 9.29 | 9.14, 9.17, 9.18, 9.22, 9.24 |
| 19-23 Nov | (M-F) | No class, Thanksgiving Recess | |||
| 36 | 26 Nov | (M) | 9.6, 11.1 | ||
| Chapter 11: Proofs in Number Theory | Daily | Weekly | |||
| 37 | 28 Nov | (W) | 11.2-11.3 | 9.33 | |
| 38 | 30 Nov | (F) | 11.4 | 11.18(a) | 9.28, 9.35, 11.6, 11.7 |
| Chapter 12: Proofs in Calculus | Daily | Weekly | |||
| 39 | 3 Dec | (M) | 12.1 | 11.26(a), 11.27(a) | |
| 40 | 5 Dec | (W) | 12.1 | 12.2 | 11.26(b)(c), 11.27(b)(c), 11.53, 12.5 |
| 14 Dec | (M) | Comprehensive Final Exam | |||
[PDF] Worksheet, Day #19
[PDF] Worksheet, Day #24
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