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What Do Mathematicians Do?:
An Overview of Undergraduate Mathematics
Steven Clontz, John Estes
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Front Matter
Colophon
The Goal of This Book
1
Gearing Up
1.1
Introducing... Your Math Department!
1.1.1
Community
1.1.1.1
Math Club
1.1.1.2
Honors Societies
1.1.1.3
Department and College Events
1.1.1.4
Connect and communicate with others
1.1.2
Academic Experiences
1.1.2.1
STEM Seminar
1.1.2.2
Mathematical Research
1.1.3
Belhaven Maker Campus
1.1.4
For Engineering Majors
1.1.5
For Actuarial Science Majors
1.1.6
Double Major and Minors
1.2
How to be a successful math major/minor
1.2.1
Introduction
1.2.2
Tips for Success
1.2.3
Putting it into practice
1.3
Careers in Mathematics
1.3.1
Introduction
1.3.2
College after college
2
A whirlwind tour of mathematics
2.1
Shopping Carts and Sets
2.1.1
Introduction
2.1.2
Collections of Things
2.1.3
An empty cart
2.1.4
Venn Diagrams
2.1.5
Set Activities
2.2
A Special Triangle
2.2.1
Introduction
2.2.2
Constructing Pascal’s Triangle
2.2.3
Patterns of Pacal’s Triangle
2.3
Logically Speaking
2.3.1
Introduction
2.3.2
Gordentockles and Chimi
2.3.3
The Usefulness of Logic
2.3.4
Contrapositives
2.3.5
Knights and Knaves
2.3.6
Samurai Jack and the Wyrm
2.4
Good Arguments
2.4.1
Introduction
2.4.2
Common Arguments
2.4.2.1
Introduction
2.4.2.2
Modus Ponens
2.4.2.3
Modus Tollens
2.4.3
Common Errors
2.4.3.1
Introduction
2.4.3.2
Converse Errors
2.4.3.3
Inverse Errors
2.4.4
More Arguments
2.5
Connecting Dots
2.5.1
intro
2.5.2
Touring the City of Königsburg
2.5.3
Connectivity
2.5.4
Different Paths
3
The World of Calculus
3.1
Harnessing
\(\infty\)
3.1.1
Introduction
3.1.2
Not always unpredictable
3.1.3
Movement On Paper
3.1.4
So what is Calculus?
3.1.4.1
Introduction
3.1.4.2
Limits of Functions
3.1.4.3
Geometric Series
3.1.5
Recursive Sequences
3.2
Newton vs Leibniz
3.2.1
Introduction
3.2.2
Newton
3.2.3
Leibniz
3.2.4
The Calculus Controversy
3.3
Archimedes’ Great Idea
3.3.1
Introduction
3.3.2
Archimedes of Syracuse
3.3.3
What is this weird number?
3.3.4
Archimedes’ Estimate
3.4
Calculus in the Movies
3.4.1
Introduction
3.4.2
Numberphile’s Math and Movies
3.5
Rates of Change
3.5.1
Introduction
3.5.2
Throwing a Ball
3.5.3
Derivatives and Instantaneous Rate of Change
3.5.4
Applications of Derivatives
3.5.4.1
Introduction
3.5.4.2
More Rates of Change
3.5.4.3
Highest and Lowest
3.6
Surfaces
3.6.1
Introduction
3.6.2
Contour Plots: Connecting 2D and 3D Shapes
3.6.3
Contour
3.6.4
Quartic Surfaces
3.7
Polar Coordinates
3.7.1
Introduction
3.7.2
Converting Coordinates
3.7.3
Polar Functions
3.7.4
Polar Coordinates in Desmos
4
Worlds of Algebra
4.1
Pipe Algebra
4.2
Algebra Shapes and Groups
4.2.1
Introduction
4.2.2
Algebra’s Goal
4.2.3
A Familiar Pattern
4.2.4
What is a Group?
4.2.4.1
Introduction
4.2.4.2
Identity Elements
4.2.4.3
Inverse Elements
4.2.5
Why do we think about groups?
4.2.6
A Group of Squares
5
Discovering New Mah
5.1
The Biggest Prime
5.1.1
Introduction
5.1.2
Math Horizons
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
