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Not Just Calculus:
First-Year Introduction to Upper-Level Mathematics
David W. Lyons
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Front Matter
Colophon
Preface
About the author
1
Basic Tools
1.1
Sets and Functions
1.1
Exercises
1.2
Properties of Functions
1.2
Exercises
1.3
Divisibility and Modular Arithmetic
1.3
Exercises
1.4
Linear and Exponential Growth
1.4
Exercises
1.5
Problems
1.5.1
Linear and Exponential Growth
1.5.1
Exercises
1.5.2
Rational and Irrational Numbers
1.5.2
Exercises
1.5.3
More Sets and Functions
1.5.3
Exercises
1.5.4
Pythagorean Triples
1.5.4
Exercises
2
The Plane
2.1
Linear Operations
2.1
Exercises
2.2
Linear Mappings
2.2
Exercises
2.3
Complex Numbers
2.3
Exercises
2.4
Problems
2.4.1
Some basic algebra and geometry in the plane
2.4.1
Exercises
2.4.2
Roots of unity
2.4.2
Exercises
2.4.3
Linear fractional transformations of the extended real numbers
2.4.3
Exercises
2.4.4
Integral points on the unit circle
2.4.4
Exercises
Back Matter
Index
Notation
Not Just Calculus:
First-Year Introduction to Upper-Level Mathematics
David W. Lyons
Department of Mathematical Sciences
Lebanon Valley College
Annville, PA, USA
lyons@lvc.edu
©2023 David W. Lyons
May 2024 Edition, revised: November 14, 2024
Colophon
Preface
About the author
