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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
1.1
Exercises
1.2
Functions
1.2
Exercises
1.3
Injectivity and Surjectivity
1.3
Exercises
1.4
Partitions and Counting
1.4
Exercises
1.5
Divisibility and Primes
1.5
Exercises
1.6
Modular Arithmetic
1.6
Exercises
1.7
Linear and Exponential Growth
1.7
Exercises
1.8
Problems
1.8.1
Linear and Exponential Growth
1.8.1
Exercises
1.8.2
Rational and Irrational Numbers
1.8.2
Exercises
1.8.3
More Sets and Functions
1.8.3
Exercises
1.8.4
Pythagorean Triples
1.8.4
Exercises
2
Planar Algebra and Geometry
2.1
The Cartesian Plane
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
January 2025 Edition, revised: February 18, 2025
Colophon
Preface
About the author
