Numerical Methods for Physics (2nd Edition)

"DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology." --Amazon Title Page Copyright Page Contents Preface Chapter 01: Speaking Mathematically 1.1: Variables (C) 1.2: The Language of Sets (C) 1.3: The Language of Relations and Functions (C) 1.4: The Language of Graphs (M) (S) Chapter 02: The Logic of Compound statements 2.1: Logical Form and Logical Equivalence (C) 2.2: Conditional Statements (C) 2.3: Valid and Invalid Arguments (C) 2.4: Application: Digital Logic Circuits (S) 2.5: Application: Number Systems and Circuits for Addition (M) (S) Chapter 03: The Logic of Quantified Statements 3.1: Predicates and Quantified Statements I (C) 3.2: Predicates and Quantified Statements II (C) 3.3: Statements with Multiple Quantifiers (C) (M) (S) 3.4: Arguments with Quantified Statements (C) Chapter 04: Elementary Number theory and Methods of Proof 4.1: Direct Proof and Counterexample I: Introduction (C) 4.2: Direct Proof and Counterexample II: Writing Advice (C) 4.3: Direct Proof and Counterexample III: Rational Numbers (C) 4.4: Direct Proof and Counterexample IV: Divisibility (C) 4.5: Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem (C) 4.6: Direct Proof and Counterexample VI: Floor and Ceiling (M) 4.7: Indirect argument: Contradiction and Contraposition (C) 4.8: Indirect Argument: Two Famous Theorems (M) 4.9: Application: The Handshake Theorem (M) 4.10: Application: Algorithms (S) Chapter 05: Sequences, Mathematical induction, and recursion 5.1: Sequences (C) (S) 5.2: Mathematical Induction I: proving Formulas (C) 5.3: Mathematical Induction II: Applications (M) 5.4: Strong Mathematical Induction and the Well-Ordering Principle for the Integers (M) 5.5: Application: Correctness of Algorithms (S) 5.6: Defining Sequences Recursively (C) 5.7: Solving Recurrence Relations by Iteration (C) 5.8: Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients (M) 5.9: General Recursive Definitions and Structural Induction (S) Chapter 06: Set Theory 6.1: Set Theory: Definitions and the Element Method of Proof (C) (S) 6.2: Properties of Sets (M) 6.3: Disproofs and Algebraic Proofs (M) 6.4: Boolean Algebras, Russell’s Paradox, and the Halting Problem (M) (S) Chapter 07 Properties of Functions 7.1: Functions Defined on General Sets (C) (S) 7.2: One-to-One, Onto, and Inverse Functions (C) (S) 7.3: Composition of Functions 7.4: Cardinality with Applications to Computability (M) (S) Chapter 08: Properties of Relations 8.1: Relations on Sets (C) 8.2: Reflexivity, Symmetry, and Transitivity (C) 8.3: Equivalence Relations (C) 8.4: Modular Arithmetic with Applications to Cryptography (M) (S) 8.5: Partial Order Relations (M) (S) Chapter 09: Counting and Probability 9.1: Introduction to Probability (C) 9.2: Possibility Trees and the Multiplication rule (C) 9.3: Counting elements of Disjoint Sets: The Addition rule (C) (S) 9.4: The Pigeonhole Principle (C) 9.5: Counting Subsets of a Set: Combinations (M) 9.6: r-Combinations with repetition Allowed (M) 9.7: Pascal’s Formula and the Binomial Theorem (M) 9.8: Probability Axioms and expected Value (M) 9.9: Conditional Probability, Bayes’ Formula, and independent events (M) Chapter 10: Theory of graphs and Trees 10.1: Trails, Paths, and Circuits (C) (S) 10.2: Matrix Representations of Graphs (M) 10.3: Isomorphisms of Graphs (M) 10.4: Trees: Examples and Basic Properties (C) (S) 10.5: Rooted Trees (M) (S) 10.6: Spanning Trees and a Shortest Path Algorithm (S) Chapter 11: Analysis of Algorithm Efficiency 11.1: Real-Valued Functions of a Real Variable and Their Graphs (C) 11.2: Big-O, Big-Omega, and Big-Theta Notations (C) 11.3: Application: Analysis of Algorithm Efficiency I (S) 11.4: Exponential and Logarithmic Functions: Graphs and Orders (M) 11.5: Application: Analysis of Algorithm Efficiency II (S) Chapter 12: Regular Expressions and Finite-State Automata 12.1: Formal Languages and Regular Expressions (C) (S) 12.2: Finite-State Automata (C) (S) 12.3: Simplifying Finite-State Automata (M) (S) Appendix Appendix A: Properties of the Real Numbers Appendix B: Solutions and Hints to Selected Exercises Index