Online courses directory (418)

Want to be an engineer or scientist? Lack mathematical confidence? Learn to think mathematically and explore essential concepts.

GMAT Math: 1. GMAT Math: 2. GMAT Math: 3. GMAT Math: 4. GMAT Math: 5. GMAT: Math 6. GMAT: Math 7. GMAT: Math 8. GMAT: Math 9. GMAT: Math 10. GMAT: Math 11. GMAT: Math 12. GMAT: Math 13. GMAT: Math 14. GMAT: Math 15. GMAT: Math 16. GMAT: Math 17. GMAT: Math 18. GMAT: Math 19. GMAT Math 20. GMAT Math 21. GMAT Math 22. GMAT Math 23. GMAT Math 24. GMAT Math 25. GMAT Math 26. GMAT Math 27. GMAT Math 28. GMAT Math 29. GMAT Math 30. GMAT Math 31. GMAT Math 32. GMAT Math 33. GMAT Math 34. GMAT Math 35. GMAT Math 36. GMAT Math 37. GMAT Math 38. GMAT Math 39. GMAT Math 40. GMAT Math 41. GMAT Math 42. GMAT Math 43. GMAT Math 44. GMAT Math 45. GMAT Math 46. GMAT Math 47. GMAT Math 48. GMAT Math 49. GMAT Math 50. GMAT Math 51. GMAT Math 52. GMAT Math 53. GMAT Math 54.

By Luca Trevisan

This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.

A short intervention designed to change students' relationships with math - this course is for teachers of math (K-12) or for other helpers of students, such as parents.

A short intervention designed to change students' relationships with math - this course is for teachers of math (K-12) or for other helpers of students, such as parents.

Questions from previous IIT JEEs. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example.

In this class you will look behind the scenes of image and video processing, from the basic and classical tools to the most modern and advanced algorithms.

In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices.

Une fonction discontinue peut-elle être solution d'une équation différentielle? Comment définir rigoureusement la masse de Dirac (une "fonction" d'intégrale un, nulle partout sauf en un point) et ses dérivées? Peut-on définir une notion de "dérivée d'ordre fractionnaire"? Cette initiation aux distributions répond à ces questions - et à bien d'autres.

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

This course is taught so that students will acquire a solid foundation in algebra. The course concentrates on the various functions that are important to the study of calculus.

This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.

Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.

Le cours expose la théorie de Galois, du classique critère de non-résolubilité des équations polynomiales aux méthodes plus avancées de calcul de groupes de Galois par réduction modulo un nombre premier.

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space.

MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.

This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.

Acknowledgements

The course materials were developed jointly by Prof. Stephen Boyd (Stanford), who was a visiting professor at MIT when this course was taught, and Prof. Lieven Vanderberghe (UCLA).

This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.