Mathematics Textbooks and Full Courses

244 affiliated resources

Mathematics Textbooks and Full Courses Collection Resources (244)

View
Selected filters:
Abstract Algebra II
Conditions of Use:
Read the Fine Print
Rating

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
Date Added:
11/11/2011
Advanced Partial Differential Equations with Applications, Fall 2009
Conditions of Use:
Remix and Share
Rating

" 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.
Date Added:
01/01/2009
Advanced Statistics
Conditions of Use:
Read the Fine Print
Rating

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
Date Added:
08/28/2013
Algebra
Conditions of Use:
Read the Fine Print
Rating

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
Date Added:
08/28/2013
Algebra2Go - Prealgebra
Conditions of Use:
Remix and Share
Rating

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
Date Added:
04/10/2013
Algebra2go:  Decimals
Conditions of Use:
Remix and Share
Rating

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
Date Added:
03/24/2014
Algebra2go- PreAlgebra - Intro to Subtraction
Conditions of Use:
Remix and Share
Rating

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
Date Added:
05/28/2013
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
Date Added:
03/03/2014
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
Date Added:
08/28/2013
Algebra II, Spring 2011
Conditions of Use:
Remix and Share
Rating

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
Date Added:
01/01/2011
Algebraic Combinatorics, Spring 2009
Conditions of Use:
Remix and Share
Rating

" 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
Date Added:
01/01/2009
Algebraic Geometry, Spring 2009
Conditions of Use:
Remix and Share
Rating

" 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
Date Added:
01/01/2009
Algebraic Topology II, Spring 2006
Conditions of Use:
Remix and Share
Rating

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
Date Added:
01/01/2006
Analysis I, Fall 2010
Conditions of Use:
Remix and Share
Rating

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
Date Added:
01/01/2010
Analysis II, Fall 2005
Conditions of Use:
Remix and Share
Rating

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
Date Added:
01/01/2005
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
Date Added:
03/31/2016
Applied Geometric Algebra, Spring 2009
Conditions of Use:
Remix and Share
Rating

Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Physics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Tisza, L
Date Added:
01/01/2009
Applied Probability
Conditions of Use:
Remix and Share
Rating

Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) is done using Matlab.

Subject:
Statistics and Probability
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Reading
Provider:
ArsDigita University
Provider Set:
ArsDigita University
Author:
Rajeev Surati
Tina Kapur
Date Added:
02/16/2011