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Contemporary Mathematics:
Contemporary Mathematics at Nebraska
Michelle Homp, Alyssa Seideman, Sean Gravelle, Andrew Hayes, The Mabel Elizabeth Kelly Fund
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1
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Front Matter
Colophon
Acknowledgements
Preface
1
Statistics
1.1
Statistics and Population
1.1.1
Statistics
1.1.2
Populations and Samples
1.1.3
Estimating Populations
1.1.3.1
One-sample estimation
1.1.3.2
The mark-recapture method
1.2
Random Sampling and Sampling Bias
1.2.1
Sampling Methods
1.2.2
How to Mess Things Up Before You Start (Sampling Bias)
1.2.3
Experiments
1.3
Chapter 1 Exercises
2
Describing Data
2.1
Frequency Tables and Bar Graphs
2.1.1
Categorizing Data
2.1.2
Presenting Categorical Data Graphically
2.1.3
Presenting Quantitative Data Graphically
2.2
Mean and Median
2.3
Range and Standard Deviation
2.4
Chapter 2 Exercises
3
Probability and Expected Value
3.1
Probability
3.1.1
Introduction
3.1.2
Basic Concepts
3.1.3
Discrete Probability Distributions
3.2
Expected Value
3.2.1
Expected Value
3.3
Continuous Probability Distributions
3.3.1
Continuous probability distributions
3.4
Chapter 3 Exercises
4
The Normal Distribution
4.1
The Normal Distribution Part I
4.1.1
Normal distribution model
4.1.2
The 68-95-99.7 Rule
4.2
The Normal Distribution Part II
4.2.1
Sample means and standard deviation
4.2.2
Normal Distributions and Confidence Intervals
4.3
Chapter 4 Exercises
5
Data Science
5.1
Data Science
5.1.1
What is data science?
5.1.2
Why data science is important
5.1.2.1
Common Online Data Analysis Platform (CODAP)
6
Researchers in Statistics and Data Science
6.1
Researchers in Statistics and Data Science
6.1.1
Federico Ardila
6.1.2
Mario Banuelos
6.1.3
Carla Cotwright-Williams
6.1.4
Lesly Goh
6.1.5
Jordan Harrod
6.1.6
Jeffrey T. Leek
6.1.7
Racine Ly
6.1.8
Jane Meza
6.1.9
Mollie Orshansky
6.1.10
Donald Richards
6.1.11
Talitha Washington
7
Ranked Voting Theory
7.1
Introduction to Ranked Voting Theory
7.1.1
Preference Schedules
7.1.2
Plurality and Its Problems
7.1.2.1
The Plurality Method
7.1.2.2
Insincere Voting
7.1.2.3
Runoff Elections
7.1.3
Ranked Voting Systems and Fairness
7.2
Alternative Voting Methods
7.2.1
The Borda Count
7.2.2
The Method of Instant Runoff Voting (IRV)
7.2.3
The Method of Pairwise Comparisons
7.3
Fairness Criteria
7.3.1
The Majority Criterion
7.3.2
The Condorcet Criterion
7.3.3
The Monotonicity Criterion
7.3.4
The Independence of Irrelevant Alternatives Criterion (IIA)
7.4
Arrow’s Theorem, Conclusions and Exercises
7.4.1
Arrow’s Impossibility Theorem
7.4.2
Chapter 7 Exercises
8
Voter Representation
8.1
Weighted Voting
8.1.1
Beginnings
8.1.2
A Look at Power
8.1.3
Calculating Power: Banzhaf Power Index
8.2
Gerrymandering
8.2.1
Government Representation and Gerrymandering
8.2.2
Using Mathematics to Combat Gerrymandering
8.2.2.1
Compactness
8.2.2.2
Efficiency Gaps
8.2.3
The Impact of Gerrymandering
8.2.4
Changing the Game
8.2.5
The Research Continues
9
Methods of Fair Division
9.1
The Sealed Bids Method of Fair Division
10
Researchers in Voting and Voter Representation
10.1
Researchers in Voting Theory and Voter Representation
10.1.1
John Banzhaf
10.1.2
Moon Duchin
10.1.3
Ranthony A.C. Edmonds
10.1.4
Gregory Herschlag
10.1.5
Andrés Jiménez-Losada
10.1.6
Nancy Rodriguez
10.1.7
Belin Tsinnajinnie
10.1.8
Ellen Veomett
11
Growth and Finance
11.1
Linear Growth
11.1.1
Linear Growth
11.1.2
When good models go bad
11.2
Exponential Growth
11.2.1
Exponential Growth
11.2.2
Logistic Growth
12
Compound Interest
12.1
Compound Interest
12.1.1
Simple Interest
12.1.2
Compound Interest
13
Disease Modeling
13.1
Modeling the Spread of an Illness
13.2
Chapter 13 Exercises
13.2.1
Section 13.1 Homework
13.2.2
Section 13.2 Homework
13.2.3
Section 13.3 Homework
14
Researchers in Modeling and Applied Mathematics
14.1
Researchers in Modeling and Applied Mathematics
14.1.1
Selenne Bañuelos
14.1.2
Ron Buckmire
14.1.3
Ricardo Cortez
14.1.4
Sara Del Valle
14.1.5
Raegan Higgins
14.1.6
Jennifer Mueller
14.1.7
Omayra Ortega
14.1.8
Freda Porter
14.1.9
Candice Price
14.1.10
Vanessa Rivera Quiñones
14.1.11
Luis Sordo Vieira
14.1.12
Richard G. White
14.1.13
Kamuela Yong
15
Graph Theory: Introduction and Euler Paths and Circuits
15.1
Introduction to Graph Theory
15.2
Euler Circuits and Kwan’s Mail Carrier Problem
15.3
Chapter 15 Exercises
15.3.1
Section 15.1 Homework
15.3.2
Section 15.2 Homework
16
Graph Theory: Hamilton Circuits and the Traveling Salesperson Problem
16.1
Hamilton Circuits and the Traveling Salesperson Problem
16.2
Chapter 16 Exercises
16.2.1
Section 16.1 Exercises
16.2.2
Section 16.2 Exercises
17
Bipartite Graphs
17.1
Bipartite Graphs and Stable Matchings
17.1.1
Bipartite Graphs
17.1.2
Matchings
17.1.3
Stable Matchings
18
Graph Theory: Networks
18.1
Networks and Minimal Spanning Trees
18.1.1
Networks and Trees
18.1.2
Spanning Trees
18.2
Chapter 18 Exercises
19
Researchers in Graph Theory
19.1
Researchers in Graph Theory
19.1.1
Jacqueline Akinpelu
19.1.2
Christina Eubanks-Turner
19.1.3
Christine Kelley
19.1.4
Steven Klee
19.1.5
Hiram H. Lopez Valdez
19.1.6
Sang-il Oum
19.1.7
John Urschel
19.1.8
Mariel Vazquez
19.1.9
Michael Young
Back Matter
A
Spreadsheet Software Tutorial
A.1
How to make a bar graph in Microsoft Excel
A.2
How to make a bar graph in Google Sheets
A.3
How to compute the mean and standard deviation in both Microsoft Excel and Google Sheets
A.4
Another appendix
🔗
Chapter
16
Graph Theory: Hamilton Circuits and the Traveling Salesperson Problem
16.1
Hamilton Circuits and the Traveling Salesperson Problem
16.2
Chapter 16 Exercises
