Mathematics Textbooks and Full Courses

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Mathematics Textbooks and Full Courses Collection Resources (278)

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Abstract Algebra II
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This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Advanced Algebra II: Activities and Homework
Conditions of Use:
No Strings Attached
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This is the main text of Kenny Felder's course in Advanced Algebra II. It consists of a series of worksheets, some intended to be used in class as group activities, and some intended to be used as homework assignments. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Teacher's Guide" collections to make up the entire course.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Advanced Algebra II: Teacher's Guide
Conditions of Use:
No Strings Attached
Rating

This is the Teacher's Guide for Kenny Felder's course in Advanced Algebra II. This guide is *not* an answer key for the homework problems: rather, it is a day-by-day guide to help the teacher understand how the author envisions the materials being used. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Homework and Activities" collections (coming soon) to make up the entire course.

Subject:
Algebra
Material Type:
Full Course
Teaching/Learning Strategy
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Advanced Partial Differential Equations with Applications, Fall 2009
Conditions of Use:
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" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosales, Rodolfo R.
Advanced Statistics
Conditions of Use:
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This course is oriented toward US high school students. The course is divided into 10 units of study. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra
Conditions of Use:
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This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra2Go - Prealgebra
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Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.

Subject:
Algebra
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go:  Decimals
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Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lecture
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go- PreAlgebra - Intro to Subtraction
Conditions of Use:
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This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go: Pre-algebra Conversions
Conditions of Use:
No Strings Attached
Rating

This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Lecture
Unit of Study
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra I
Conditions of Use:
Read the Fine Print
Rating

This course is oriented toward US high school students. Its structure and materials are aligned to the US Common Core Standards. Foci include: graphing, equations and inequalities.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra II, Spring 2011
Conditions of Use:
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This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Algebraic Combinatorics, Spring 2009
Conditions of Use:
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" This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Musiker, Gregg
Algebraic Geometry, Spring 2009
Conditions of Use:
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" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kedlaya, Kiran
Algebraic Topology II, Spring 2006
Conditions of Use:
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In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Behrens, Mark
Analysis I, Fall 2010
Conditions of Use:
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Wehrheim, Katrin
Analysis II, Fall 2005
Conditions of Use:
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Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, n-dimensional version of Stokes' theorem. 18.901 helpful but not required.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Guillemin, Victor
Applied Calculus
Conditions of Use:
No Strings Attached
Rating

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Subject:
Calculus
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Dale Hoffman
David Lippman
Shana Calaway