This course focuses on linear ordinary differential equations (or ODEs) and will introduce several other subclasses and their respective properties. Despite centuries of study, numerical approximation is the only practical approach to the solution of complicated ODEs that has emerged; this course will introduce you to the fundamentals behind numerical solutions. Upon successful completion of this course, students will be able to: Identify ordinary differential equations and their respective orders; Explain and demonstrate how differential equations are used to model certain situations; Solve first order differential equations as well as initial value problems; Solve linear differential equations with constant coefficients; Use power series to find solutions of linear differential equations, Solve linear systems of differential equations with constant coefficients; Use the Laplace transform to solve initial value problems; Use select methods of numerical approximation to find solutions to differential equations. (Mathematics 221; See also: Mechanical Engineering 003)

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

Table of Contents
Systems of Linear Equations
Vectors
Matrices
Vector Spaces
Determinants
Eigenvalues
Linear Transformations
Representations
Preliminaries
Reference

Access also available here: http://linear.ups.edu/

After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.

Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.

The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Content varies from year to year. Introduces new and significant developments in algebraic topology with the focus on homotopy theory and related areas. Spring 2003: An introduction to higher algebraic K-theory.

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills.Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.

Table of Contents
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 Polynomials
7 Graphing Linear Equations and Inequalities in One and Two Variables
8 Rational Expressions
9 Roots, Radicals, and Square Root Equations
10 Quadratic Equations
11 Systems of Linear Equations
12 Appendix

A community college level textbook that provides non-STEM students with a high-quality and academically rigorous book.

PowerPoint Slides to accompany Chapter 2 of OpenStax College Algebra textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax College Algebra textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Table of Contents:

Chapter 1: Algebra Review
Introduction to Algebra Review
Section 1.1 Functions
Section 1.2 Operations on Functions
Section 1.3 Linear Functions
Section 1.4 Exponents
Section 1.5 Quadratics
Section 1.6 Polynomials and Rational Functions
Section 1.7 Exponential Functions
Section 1.8: Logarithmic Functions
Chapter 1 Review Exercises
Chapter 1 Review Problems

Chapter 2: Limits and The Derivative
Introduction to Limits
Section 2.1: Limits and Continuity
Introduction to the Derivative
Section 2.2: The Derivative
Section 2.3: The Power and Sum Rules for Derivatives
Section 2.4: Product and Quotient Rules
Section 2.5: Chain Rule
Section 2.6: Second Derivative and Concavity
Chapter 2 Review Exercises: Limits
Chapter 2 Review Exercises: The Derivative
Chapter 2 Review Problems

Chapter 3: Applications of the Derivative
Introduction to Applications of the Derivative
Section 3.1: Optimization
Section 3.2: Curve Sketching
Section 3.3: Applied Optimization
Section 3.4: Other Applications
Section 3.5: Implicit Differentiation and Related Rates
Chapter 3 Review Exercises
Chapter 3 Review Problems
Chapter 3 Solutions to Review Problems

Chapter 4: The Integral
Introduction to the Integral
Section 4.1: The Definite Integral
Section 4.2: The Fundamental Theorem and Antidifferentiation
Section 4.3: Antiderivatives of Formulas
Section 4.4: Substitution
Section 4.5: Average Value and the Net Change Theorem
Section 4.6: Applications to Business
Chapter 4 Review Exercises
Chapter 4 Review Problems

This textbook was created through Connecting the Pipeline: Libraries, OER, and Dual Enrollment from Secondary to Postsecondary, a $1.3 million project funded by LOUIS: The Louisiana Library Network and the Institute of Library and Museum Services. This project supports the extension of access to high-quality post-secondary opportunities to high school students across Louisiana and beyond by creating materials that can be adopted for dual enrollment environments. Dual enrollment is the opportunity for a student to be enrolled in high school and college at the same time.

The cohort-developed OER course materials are released under a license that permits their free use, reuse, modification and sharing with others. This includes a corresponding course available in Moodle and Canvas that can be imported to other platforms.

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.

Access also available here: https://academicworks.cuny.edu/qb_oers/15/

Table of Contents
Linear Equations And Inequalities

GPS 1: Understanding Linear Equations
GPS 2: Solving Linear Equations With Whole Numbers
GPS 3: Adding Signed Numbers
GPS 4: Subtracting Signed Numbers
GPS 5: Multiplying And Dividing Signed Numbers
GPS 6: Solving Linear Equations With Signed Numbers
GPS 7: Translating Words Into Expressions And Equations
GPS 8: Solving Linear Inequalities, Part 1
GPS 9: Solving Linear Inequalities, Part 2
GPS 10: Solving Linear Equations With Fractions
GPS 11: More Linear Equations With Fractions
GPS 12: Solving Literal Linear Equations
The Coordinate Plane And Lines

GPS 13: Introduction To The Coordinate Plane
GPS 14: Intercepts Of A Line
GPS 15: Slope And Equations Of A Line
GPS 16: The Slope-Intercept Equation Of A Line
GPS 17: Slope-Intercept Equation And Graphing
GPS 18: Graphing Lines In Slope-Intercept Form
GPS 19: Finding An Equation Of A Line From Its Graph
GPS 20: Horizontal And Vertical Lines
Systems Of Linear Equations

GPS 21: Introduction To Systems Of Linear Equations And Solving Graphically
GPS 22: More On Solving Systems Graphically
GPS 23: Solving Systems Of Linear Equations Algebraically
GPS 24: More On Solving Systems Algebraically
Exponents

GPS 25: Rules Of Exponents, Part 1
GPS 26: Rules Of Exponents, Part 2
Polynomials And Operations

GPS 27: Introduction To Polynomials And Operations
GPS 28: Multiplying Polynomials
GPS 29: Removing The Greatest Common Factor
GPS 30: Factoring By Grouping
GPS 31: Factoring Trinomials By Grouping – Part 1
GPS 32: Factoring Trinomials By Grouping – Part 2
GPS 33: Factoring Trinomials By Grouping – Part 3
GPS 34: Factoring Trinomials By Grouping – Part 4
GPS 35: Factoring A Difference Of Squares
GPS 36: Multistep Factoring
GPS 37: Solving Quadratic Equations By Factoring
Algebraic Expressions

GPS 38: Evaluating Algebraic Expressions
Square Roots And Operations

GPS 39: Introduction To Square Roots
GPS 40: Operations With Square Roots
GPS 41: Pythagorean Theorem

College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended).

Table of Contents
1 Relations and Functions
2 Linear and Quadratic Functions
3 Polynomial Functions
4 Rational Functions
5 Further Topics in Functions
6 Exponential and Logarithmic Functions
7 Hooked on Conics
8 Systems of Equations and Matrices
9 Sequences and the Binomial Theorem

Table of Contents
Chapter One: Solving Linear Systems
Chapter Two: Vector Spaces
Chapter Three: Maps Between Spaces
Chapter Four: Determinants
Chapter Five: Similarity

About the Book
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges.

Access also available here: http://joshua.smcvt.edu/linearalgebra/

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

Topics vary from year to year. Fall Term: Numerical properties and vanish theorems for ample, nef, and big line bundles and vector bundles; multiplier ideals and their applications

Seminar for mathematics majors. Students present and discuss the subject matter and write up exercises. Topic for Fall 2002: Classical geometry, beginning with Euclid's Elements and continuing to applications of Galois theory that solve the geometry problems of antiquity. No prior knowledge of Galois theory required. Instruction and practice in oral communication provided.