This course introduces the student to the study of linear algebra. Practically every modern technology relies on linear algebra to simplify the computations required for internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between. Upon completion of this course, the student will be able to: Define and identify linear equations; Write a system of equations in matrix-vector form; Explain the geometric interpretation of a system of linear equations; Solve linear equations using a variety of methods; Define general, particular, and homogeneous solutions; Identify how many solutions a linear system has; Correctly manipulate vectors algebraically and perform matrix-vector and matrix-matrix multiplication; Define linear combination and span; Define and distinguish between singular and nonsingular matrices and calculate a matrix inverse; Define and compute LU decompositions; Relate invertibility of matrices to solvability of linear systems; Define and characterize Euclidean space; Define and compute dot and cross-products; Define and identify vector spaces and subspaces; Define spanning set and determine the span of a set of vectors; Define and verify linear independence; Define basis and dimension; Show that a set of vectors is a basis; Define and compute column space, row space, nullspace, and rank; Define and identify isomorphisms and homomorphisms; Use row and column space to solve linear systems; State the rank-nullity theorem; Define inner product, inner product space, and orthogonality; Interpret inner products geometrically; Define determinants using the permutation expansion; State the properties of determinants, such as that the determinant of the product is the product of the determinants; Compute the determinant using cofactor expansions, row reduction, and Cramer's Rule; Define and compute the characteristic polynomial of a matrix; Define and compute eigenvalues and eigenvectors; Explain the geometric significance of eigenvalues and eigenvectors; Define similarity and diagonalizability; Identify similar matrices; Identify some necessary conditions for diagonalizability. (Mathematics 211; See also: Computer Science 105)

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.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

Linear Algebra is both rich in theory and full of interesting applications; in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. Upon successful completion of this course, the student will be able to: Solve systems of linear equations; Define the abstract notions of vector space and inner product space; State examples of vector spaces; Diagonalize a matrix; Formulate what a system of linear equations is in terms of matrices; Give an example of a space that has the Archimedian property; Use the Euclidean algorithm to find the greatest common divisor; Understand polar form and geometric interpretation of the complex numbers; Explain what the fundamental theorem of algebra states; Determine when two matrices are row equivalent; State the Fredholm alternative; Identify matrices that are in row reduced echelon form; Find a LU factorization for a given matrix; Find a PLU factorization for a given matrix; Find a QR factorization for a given matrix; Use the simplex algorithm; Compute eigenvalues and eigenvectors; State Shur's Theorem; Define normal matrices; Explain the composition and the inversion of permutations; Define and compute the determinant; Explain when eigenvalues exist for a given operator; Normal form of a nilpotent operator; Understand the idea of Jordan blocks, Jordan matrices, and the Jordan form of a matrix; Define quadratic forms; State the second derivative test; Define eigenvectors and eigenvalues; Define a vector space and state its properties; State the notions of linear span, linear independence, and the basis of a vector space; Understand the ideas of linear independence, spanning set, basis, and dimension; Define a linear transformation; State the properties of linear transformations; Define the characteristic polynomial of a matrix; Define a Markov matrix; State what it means to have the property of being a stochastic matrix; Define a normed vector space; Apply the Cauchy Schwarz inequality; State the Riesz representation theorem; State what it means for a nxn matrix to be diagonalizable; Define Hermitian operators; Define a Hilbert space; Prove the Cayley Hamilton theorem; Define the adjoint of an operator; Define normal operators; State the spectral theorem; Understand how to find the singular-value decomposition of an operator; Define the notion of length for abstract vectors in abstract vector spaces; Define orthogonal vectors; Define orthogonal and orthonormal subsets of R^n; Use the Gram-Schmidt process; Find the eigenvalues and the eigenvectors of a given matrix numerically; Provide an explicit description of the Power Method. (Mathematics 212)

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.

This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.

The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.

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).

An introduction to algebra covering solving and graphing linear equations, polynomials, factoring, and rational expressions

This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

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

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.

" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."

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.

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.

PowerPoint Slides to accompany Chapter 3 (Sections 3.1, 3.2 and 3.3) 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.

PowerPoint Slides to accompany Chapter 3 (Sections 3.4, 3.5 and 3.7) 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.

PowerPoint Slides to accompany Chapter 4 (Sections 4.1 and 4.2) 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.

PowerPoint Slides to accompany Chapter 5 (Sections 5.1, 5.2, 5.3 and 5.6) 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.

PowerPoint Slides to accompany Chapter 6 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.

PowerPoint Slides to accompany Chapter 7 (Section 7.1 only) 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.

Table of Contents
1 Whole Numbers
2 The Language of Algebra
3 Integers
4 Fractions
5 Decimals
6 Percents
7 The Properties of Real Numbers
8 Solving Linear Equations
9 Math Models and Geometry
10 Polynomials
11 Graphs

Access also available here: https://openstax.org/details/books/prealgebra