For freshman/sophomore one-semester introductory courses in discrete math
that include intermediate programming for computer science and mathematics
This brief introduction to the mathematics of computer science prepares
students for the math they will encounter in later courses. With applications
that are specific to computer science, this text helps students develop
reasoning skills and provides them with an early introduction to fundamental
mathematics necessary for future math and computer science courses.
Table of Contents
0. Notes on Proofs.
Propositional Logic. Implication. Direct Proof.
The Contrapositive. Proof by Contradiction. If And Only If.
What Are Sets? New Sets from Old. Properties of
Sets. A Paradox. Large Collection of Sets.
2. Functions and Relations.
Exponential and Log Functions. Floor and Ceiling
3. Boolean Algebra.
Propositional Logic. Sets. Boolean Algebras.
Some Boolean Algebra Theorems. Switching Circuits. Storing Numbers in a Digital
Computer. Circuitry to Add.
4. Natural Numbers and Induction.
Well-ordering and Mathematical Induction.
Well-ordering Implies Mathematical Induction. The Peano Axioms.
5. Number Theory.
The Division Theorem. Greatest Common Divisors.
Primes. Modular Arithmetic. A Cryptological Example. Modular Multiplication and
Division. More Cryptology. Fermat's Little Theorem. Fast Exponentiation. Euler's
Theorem. RSA Encryption.
Binary Search. Euclid's Algorithm. Tower of
7. Solving Recurrences.
The Rules of Sum and Product. Permutations.
Combinations. Calculation Considerations. The Binomial Theorem. Applications of
Counting to Probability.
Matrix Operations. Systems of Equations. The
Determinant. Gaussian Elimination. Computing Multiplicative Inverses. Encryption
Euler Circuits and Tours. Symbols and Terms for
Graphs. A Return to Euler Circuits. Minimal Spanning Tree. Some Programming