## Open Educational Resources ## Open Educational Resources for Mathematics

#### Title

Contemporary Mathematics: Contemporary Mathematics at Nebraska

8-26-2019

Article

#### Citation

An Open Educational Resource.

This work is supported in part by a grant from the Mabel Elizabeth Kelly Fund to promote the improvement of teaching at the University of Nebraska-Lincoln

#### Abstract

MATH 203 Contemporary Mathematics is designed for students who are not majoring in mathematics and is intended to serve as a general education math class. The standard high school progression of algebra - geometry - more algebra - precalculus - calculus can leave many students with a distaste for math, partly because it gives the impression that mathematics is all about algebraic manipulations, and partly because it omits many areas of interesting mathematics needed for personal use or informed citizenship. MATH 203 tries to fill those gaps by covering a wide range of mathematical topics, of which algebra is only a small piece. The mathematical content that we hope students will find both interesting and useful has been divided into four units: statistics, social choice (such as voting theory and fair division), growth and finance, and graph theory.

The text is intended to be supplemented for the Math 203 Course Manual available for purchase at the UNL Bookstore.

1 Statistics •

Statistics and Population • Random Sampling and Sampling Bias • Chapter 1 Exercises

2 Describing Data • Frequency Tables and Bar Graphs • Mean and Median • Range and Standard Deviation • Chapter 2 Exercises

3 Probability and Expected Value • Probability • Expected Value • Chapter 3 Exercises

4 The Normal Distribution • The Normal Distribution Part I • The Normal Distribution Part II • Chapter 4 Exercises

5 Ranked Voting Theory • Introduction to Ranked Voting Theory • The Borda Count and the Majority Criterion • Instant Runoff Voting and the Monotonicity Criterion • Pairwise Comparisons and the Condorcet Criterion • Independence of Irrelevant Alternatives and Arrow's Theorem • Chapter 5 Exercises

6 Power in Weighted Voting Systems • Weighted Voting

7 Methods of Fair Division • The Sealed Bids Method of Fair Division • The Adjusted Winner Procedure for Fair Division

8 Disease Modeling • Modeling the Spread of an Illness • Chapter 8 Exercises

9 Growth and Finance • Linear Growth • Exponential Growth • Back Matter