Online courses directory (418)

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions. 

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

Prepare for the College Mathematics CLEP Exam through Education Portal's brief video lessons on mathematics. This course covers topics ranging from real number systems to probability and statistics. You'll learn to use the midpoint and distance formulas, graph inequalities and multiply binomials. You'll also explore the properties of various shapes and learn to determine their area and perimeter. Our lessons are taught by professional educators with experience in mathematics. In addition to designing the videos in this course, these educators have developed written transcripts and self-assessment quizzes to round out your learning experience.

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.

This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Algebra+ is a 10-week online course designed for students who have successfully completed high school algebra but who placed into pre-college level mathematics at their local college or university. This course is for refreshing their math skills with a review of pre-college level algebra. After successfully completing this course, the goal would be to retake your college

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.

Prepare for the College Mathematics CLEP Exam through Education Portal's brief video lessons on mathematics. This course covers topics ranging from real number systems to probability and statistics. You'll learn to use the midpoint and distance formulas, graph inequalities and multiply binomials. You'll also explore the properties of various shapes and learn to determine their area and perimeter. Our lessons are taught by professional educators with experience in mathematics. In addition to designing the videos in this course, these educators have developed written transcripts and self-assessment quizzes to round out your learning experience.

The key learning objectives of this MOOC are: 1. Review, develop, and demonstrate their conceptual understanding and procedural skills with selected fundamental mathematical topics 2. Collaborate with peers to solve problems that arise in mathematics and other contexts 3. Create and use representations to organize, record, and communicate mathematical ideas 4. Reflect on the process of problem solving 5. Justify results using mathematical reasoning 6. Communicate mathematical thinking clearly to peers and to the instructor The learning objectives and course content align with on?campus versions of this type of course. We are building this MOOC around key concepts and skills in the nationally recognized Common Core State Standards for Mathematics, the ACT College Readiness Standards, and the SAT Skills Insight. Students successfully completing our MOOC will find their subject matter knowledge to be in alignment with the "typical" course offered by other U.S. colleges and universities. By using Common Core standards, ACT College Readiness Standards, and the SAT Skills Insight, we can also begin to develop post?test instruments that will assess the students' levels of proficiency

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.

Sal works through 80 questions taken from the California Standards Test for Algebra II.

18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.

Topics covered in a first year course in differential equations.

This free online course is the second of our Upper-Secondary Mathematics suite of courses. It covers ratio and proportion, geometric sequences, arithmetic series, difference equations, linear programming, geometry, trigonometry, and graphs. This course is suitable for all math students revising for exams. It is also suitable for anyone with an interest in Mathematics. <br />

Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.

This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.472J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.158J.

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

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.