It is important to learn math because it makes us better people.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Author:
- Ninglu Wang
- Jessamine Bartley-Matthews
- Date Added:
- 04/09/2016

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It is important to learn math because it makes us better people.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Author:
- Ninglu Wang
- Jessamine Bartley-Matthews
- Date Added:
- 04/09/2016

Conditions of Use:

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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
- Date Added:
- 11/11/2011

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Rosales, Rodolfo R.
- Date Added:
- 01/01/2009

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
- Date Added:
- 08/28/2013

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
- Date Added:
- 08/28/2013

Conditions of Use:

No Strings Attached

In this course students gain proficiency in Linear Equations, Linear Inequalities, Graphing linear equations, Solving Systems of Equations, Simplifying with Polynomials, Division of Polynomials, Factoring Polynomials, Developing a Factoring Strategy, and Solving Other Algebraic Equations.

- Subject:
- Career and Technical Education
- Education
- Mathematics
- Material Type:
- Full Course
- Author:
- Boyoung Chae
- SBCTC Admin
- Date Added:
- 02/01/2018

Conditions of Use:

No Strings Attached

The College and Career Readiness Standards for Level E (High School) outline the outcomes for this course.In this course students gain proficiency in Functions, Linear Functions, Solving Quadratics, Quadratic Functions, Exponential Functions, and Logarithmic Functions.

- Subject:
- Career and Technical Education
- Education
- Mathematics
- Material Type:
- Full Course
- Author:
- Boyoung Chae
- SBCTC Admin
- Date Added:
- 02/01/2018

Conditions of Use:

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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

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Artin, Michael
- Date Added:
- 01/01/2011

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Kedlaya, Kiran
- Date Added:
- 01/01/2009

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Behrens, Mark
- Date Added:
- 01/01/2006

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Wehrheim, Katrin
- Date Added:
- 01/01/2010

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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Guillemin, Victor
- Date Added:
- 01/01/2005

Conditions of Use:

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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

Conditions of Use:

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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:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Tisza, L
- Date Added:
- 01/01/2009

Conditions of Use:

No Strings Attached

This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.

- Subject:
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- Rice University
- Provider Set:
- OpenStax CNX
- Author:
- Paul E. Pfeiffer
- Date Added:
- 09/18/2009

I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; well learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options.

- Subject:
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- UMass Boston
- Provider Set:
- UMass Boston OpenCourseWare
- Author:
- Eugene Gallagher
- Date Added:
- 10/14/2015

Conditions of Use:

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This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers modelintegers are only introduced at the end of the course.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Textbook
- Provider:
- Lumen Learning
- Provider Set:
- Candela Courseware
- Author:
- David Lippman
- Date Added:
- 03/31/2016

Conditions of Use:

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The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

- Subject:
- Mathematics
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Stanley, Richard
- Date Added:
- 01/01/2003

Conditions of Use:

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The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world. Our course therefore aims to broaden students’ appreciation for and understanding of how literature interacts with--both reflecting upon and contributing to--the scientific understanding of the world. We are just as centrally committed to encouraging students to regard imaginative literature as a unique contribution to knowledge in its own right, and to see literary works of art as objects that demand and richly repay close critical analysis. It is our hope that the course will serve students well if they elect to pursue further work in Literature or other discipline in SHASS, and also enrich or complement their understanding of probability and statistics in other scientific and engineering subjects they elect to take.

- Subject:
- Arts and Humanities
- Literature
- Philosophy
- Religious Studies
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Jackson, Noel
- Kibel, Alvin
- Raman, Shankar
- Date Added:
- 01/01/2008