## 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

[PDF] Final Review ... [PDF] Solutions

[PDF] Final Exam ... [PDF] Solutions