Math 311W -- Spring 2016

Concepts of Discrete Mathematics The Pennsylvania State University

Announcements
Syllabus
Suggested Homework
Quiz Solutions
 Lecture Room: 303 Willard Bldg Lecture Times: MWF 1:25 pm --2:15 pm Instructor: Dr. Larry Rolen Office: 212 McAllister Bldg Email: larryrolen@psu.edu Text: Numbers, Groups & Codes by J. F. Humphreys & M. Y. Prest, Second Edition, Cambridge University Press. ISBN number: 978-0-521-54050-6. Note: An electronic version of the book (an e-book) is available through the PSU Library. Search for the text at www.libraries.psu.edu. Office Hours: Wednesdays 2:30-3:30 pm, and Thursdays 2-3 pm, or by appointment.

Announcements For the final exam, extra office hours will be held on May 2 from 12-2.

Syllabus

This course covers basic set, number, and group theory, along with strategies of mathematical proof. We will roughly follow Chapters 1-5 in the book.

Here is an official pdf of the syllabus for this course.

Suggested Homework

Section 2.1: 1, 2, 5, 6, 7, 8, understand this joke.

Section 2.2: 1,2,4,5,6,7,10, Show that for any two open intervals (a,b) and (c,d) on the real line that there is a bijection f:(a,b)--->(c,d). (Hint: you should explicitly construct a linear function).

Section 2.3: 1,2,7,8.

Section 3.1: 1,2,3,4.

Section 3.2: 1.

Section 3.3: 1,2,3 from the book, understand the proofs that the square root of 2 is irrational, and that there are infinitely many prime numbers. Also, show that if x is an irrational, positive number, then the square root of x is also irrational.

Section 1.1: 1-7.

Section 1.2: 1-7,9.

Section 1.3: 1-8.

Section 1.4: 1-8, Determine the possible congruence classes of a square modulo 8. Important proofs from class to know: Theorems 1.4.1, 1.4.3.

Section 1.5: 1,2,3,5.

Section 1.6: 1,2,3,5,6,7,12.

Section 4.1: 1,2,3,4,5.

Section 4.2: 1-10.

Section 4.3 1,2,3,4,5,8.

Section 5.1: 1,2,3,4,5,6,8,10.

Section 5.2: 1,2,3,5.

Section 5.3: 1,2,3,4,5.

Quiz 1

Quiz 2

Quiz 3

Quiz 4

Quiz 5

Quiz 6

Quiz 7

Quiz 8

Quiz 9

Quiz 10

Quiz 11

Quiz 12

Exams

Review guide for Exam 1

Solutions to Exam 1

Review guide for Exam 2

Solutions to Exam 2

Review guide for final exam