Math 311W -- Spring 2016

Concepts of Discrete Mathematics
The Pennsylvania State University

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

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
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.


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 Solutions

Quiz 1

Quiz 2

Quiz 3

Quiz 4

Quiz 5

Quiz 6

Quiz 7

Quiz 8

Quiz 9

Quiz 10

Quiz 11

Quiz 12


Review guide for Exam 1

Solutions to Exam 1

Review guide for Exam 2

Solutions to Exam 2

Review guide for final exam

Academic Misconduct

Copying another student's work, passing off another's work as your own, using phones or calculators on quizzes or exams, having unauthorized possession of copies of exams or quizzes, other acts of deception (including lying to obtain extensions or rescheduling of homeworks, quizzes, or exams), and aiding others in cheating (e.g. letting another copy your work) are all examples of (but not the only instances of) academic misconduct and will not be tolerated under any circumstance. If you are suspected of such activity, confidential charges will be made against you and academic sanctions will be recommended against you. If you refuse to respond to such allegations within a reasonable period of time, this will be taken as an admission of guilt. If you choose to accept or contest the charges, it will be sent to the Academic Integrity Committee, and you cannot withdraw from or drop the course during this process. If you are found guilty, you will receive sanctions which may include, but are not limited to, a warning, an automatic 0 grade on an assignment, quiz, or exam, an overall reduction in the final course grade, or an automatic F in the course, depending on the severity of the offense. Furthermore, you will not be able to drop or withdraw from the course, and, for instance, cannot drop the course to avoid penalties. For further information about the procedure for such cases, please consult the Eberly College of Science Academic Integrity homepage.