Updating search results...

Mathematics Textbooks and Full Courses

589 affiliated resources

Search Resources

View
Selected filters:
Algebraic Geometry
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Bezrukavnikov, Roman
Date Added:
09/01/2015
Algebraic Geometry
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

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
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
02/01/2009
Algebraic Techniques and Semidefinite Optimization
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Parrilo, Pablo
Date Added:
02/01/2006
Algebraic Topology I
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes, Homological algebra, Cohomology, and Poincare duality.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Miller, Haynes
Date Added:
09/01/2016
Algebraic Topology II
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is the second part of the two-course series on algebraic topology. Topics include basic homotopy theory, obstruction theory, classifying spaces, spectral sequences, characteristic classes, and Steenrod operations.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Miller, Haynes
Date Added:
02/01/2020
Algorithmic Aspects of Machine Learning
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

Subject:
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Moitra, Ankur
Date Added:
02/01/2015
Algorithmic Lower Bounds: Fun with Hardness Proofs
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Subject:
Applied Science
Computer Science
Engineering
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Demaine, Erik
Date Added:
09/01/2014
Algorithms for Inference
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference.

Subject:
Applied Science
Computer Science
Engineering
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Shah, Devavrat
Date Added:
09/01/2014
Analysis I
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

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:
Calculus
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Wehrheim, Katrin
Date Added:
09/01/2010
Analysis II
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.

Subject:
Calculus
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Guillemin, Victor
Date Added:
09/01/2005
The Analytics Edge
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course presents real-world examples in which quantitative methods provide a significant competitive edge that has led to a first order impact on some of today's most important companies. We outline the competitive landscape and present the key quantitative methods that created the edge (data-mining, dynamic optimization, simulation), and discuss their impact.

Subject:
Business and Communication
Management
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Bertsimas, Dimitris
Date Added:
02/01/2017
Analytics of Finance
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course covers the key quantitative methods of finance: financial econometrics and statistical inference for financial applications; dynamic optimization; Monte Carlo simulation; stochastic (Itô) calculus. These techniques, along with their computer implementation, are covered in depth. Application areas include portfolio management, risk management, derivatives, and proprietary trading.

Subject:
Business and Communication
Economics
Finance
Mathematics
Social Science
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Kogan, Leonid
Date Added:
09/01/2010
Ancient Greek Philosophy and Mathematics
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.

Subject:
Ancient History
Arts and Humanities
English Language Arts
History
Literature
Mathematics
Philosophy
Reading Literature
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Perlman, Lee
Date Added:
02/01/2016
Applications of System Dynamics
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

15.875 is a project-based course that explores how organizations can use system dynamics to achieve important goals. In small groups, students learn modeling and consulting skills by working on a term-long project with real-life managers. A diverse set of businesses and organizations sponsor class projects, from start-ups to the Fortune 500. The course focuses on gaining practical insight from the system dynamics process, and appeals to people interested in system dynamics, consulting, or managerial policy-making.

Subject:
Applied Science
Business and Communication
Engineering
Management
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Hines, James
Date Added:
02/01/2004
Applied Calculus
Read the Fine Print
Rating
0.0 stars

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
Mathematics
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 Category Theory
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.

Subject:
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Fong, Brendan
Spivak, David
Date Added:
01/01/2019
Applied Econometrics: Mostly Harmless Big Data
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This course covers empirical strategies for applied micro research questions. Our agenda includes regression and matching, instrumental variables, differences-in-differences, regression discontinuity designs, standard errors, and a module consisting of 8–9 lectures on the analysis of high-dimensional data sets a.k.a. "Big Data".

Subject:
Applied Science
Computer Science
Economics
Engineering
Mathematics
Social Science
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Angrist, Joshua
Chernozhukov, Victor
Date Added:
09/01/2014
Applied Geometric Algebra
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

László 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. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Geometry
Mathematics
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Tisza, László
Date Added:
02/01/2009
Applied Quantum and Statistical Physics
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

6.728 is offered under the department's "Devices, Circuits, and Systems" concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

Subject:
Mathematics
Physical Science
Physics
Statistics and Probability
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Orlando, Terry
Date Added:
09/01/2006
Applied Statistics, Spring 2009
Only Sharing Permitted
CC BY-NC-ND
Rating
0.0 stars

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; we’ll 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:
Mathematics
Statistics and Probability
Material Type:
Full Course
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Eugene Gallagher
Date Added:
10/14/2015