Preface. Acknowledgments. 1 Arithmetic Review. 2 Basic Properties of Real Numbers. 3 Basic Operations with Real Numbers. 4 Algebraic Expressions and Equations. 5 Solving Linear Equations and Inequalities. 6 Factoring ...

Chapter 1: Real Numbers and Their Operations. Chapter 2: Linear Equations and Inequalities. Chapter 3: Graphing Lines. Chapter 4: Solving Linear Systems. Chapter 5: Polynomials and Their Operations. Chapter 6: Factoring ...

Chapter 1: Tools for Analysis. 1.1 Basic Concepts of Set Theory. 1.2 Functions. 1.3 The Natural Numbers and Mathematical Induction. 1.4 Order Field Axioms. 1.5 The Completeness Axiom for the Real Numbers. 1.6 Applications ...

Introduction to Writing Proofs in Mathematics. Logical Reasoning. Constructing and Writing Proofs in Mathematics. Mathematical Induction. Set Theory. Functions. Equivalence Relations. Topics in Number Theory. Finite and ...

Chapter 1: Problem Solving. Chapter 2: Voting Theory. Chapter 3: Weighted Voting. Chapter 4: Apportionment. Chapter 5: Fair Division. Chapter 6: Graph Theory. Chapter 7: Scheduling. Chapter 8: Growth Models. Chapter 9: ...

First order ODEs. Higher order linear ODEs. Systems of ODEs. Fourier series and PDEs. Eigenvalue problems. The Laplace transform. Power series methods. Nonlinear systems.

Review. Functions. Limits. Derivatives. Applications of Derivatives. Integration. Techniques of Integration. Applications of Integration. Differential Equations. Polar Coordinates, Parametric Equations.

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis ...

Chapter 1: What is Linear Algebra? Chapter 2: Systems of Linear Equations. Chapter 3: The Simplex Method. Chapter 4: Vectors in Space, n-Vectors. Chapter 5: Vector Spaces. Chapter 6: Linear Transformations. Chapter 7: ...

Chapter 1: Vectors in Euclidean Space. Chapter 2: Functions of Several Variables. Chapter 3: Multiple Integrals. Chapter 4: Line and Surface Integrals.