Online courses directory (418)

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.

The three options for 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 fulfills the MIT CI requirement.

Learn how to use regression models, the most important statistical analysis tool in the data scientist's toolkit. This is the seventh course in the Johns Hopkins Data Science Specialization.

Online course for preparing for the Quantitative section of the GRE.

“Why is math important?  Why do I have to learn math?”  These are typical questions that you have most likely asked at one time or another in your education.  While you may learn things in math class that you will not use again, the study of mathematics is still an important one for human development.  Math is widely-used in daily activities (e.g. shopping, cooking, etc.) and in most careers (e.g. medicine, teaching, engineering, construction, business, statistics in psychology, etc.).  Math is also considered a “universal language.”  One of the fundamental reasons why you learn math is to help you tackle problems, both mathematical and non-mathematical, with clear, concise, and logical steps.  In this course, you will study important fundamental math concepts. This course begins your journey into the “Real World Math” series.  These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life.  In thi…

This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals).  Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest. The subject of algebra focuses on generalizing these procedures.  For example, algebra will enable you to describe how to calculate change without specifying how much money is to be spent on a purchase-it will teach you the basic formulas and steps you need to take no matter what the specific details of the situation are.  Likewise, accountants use algebraic formulas to calculate the monthly loan payments for a loan of any size under any interest rate.  In this course, you will learn how to work with formulas that a…

“Everything is numbers.”  This phrase was uttered by the lead character, Dr. Charlie Epps, on the hit television show “NUMB3RS.”  If everything has a mathematical underpinning, then it follows that everything is somehow mathematically connected, even if it is only in some odd, “six degrees of separation (or Kevin Bacon)” kind of way. Geometry is the study of space (for now, mainly two-dimensional, with some three-dimensional thrown in) and the relationships of objects contained inside.  It is one of the more relatable math courses, because it often answers that age-old question, “When am I ever going to use this in real life?”  Look around you right now.  Do you see any triangles?  Can you spot any circles?  Do you see any books that look like they are twice the size of other books?  Does your wall have paint on it? In geometry, you will explore the objects that make up our universe.  Most people never give a second thought to how things are constructed, but there are geometric ru…

In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

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.

In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book A Survey of Minimal Surfaces, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.

This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.

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 />

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

Lectures based on the Singapore Math curriculum. You can follow along through the workbooks available at singaporemath.com. Singapore Math: Grade 3a, Unit 1 (part 1). Singapore Math: Grade 3a Unit 1 (part 2). Singapore Math: Grade 3a, Unit 1 (part 3). Singapore Math: Grade 3a, Unit 1 (part 4). Singapore Math: Grade 3a, Unit 1 (part 5). Singapore Math: Grade 3a, Unit 1 (part 6). Singapore Math: Grade 3a, Unit 1 (part 7). Singapore Math: Grade 3a, Unit 1 (part 8). Singapore Math: Grade 3a, Unit 1 (part 9). Singapore Math: Grade 3a Unit 2 (part 1). Singapore Math: Grade 3a Unit 2 (part 2). Singapore Math: Grade 3a Unit 2 (part 3). Singapore Math: Grade 3a Unit 2 (part 4). Singapore Math: Grade 3a Unit 2 (part 5). Singapore Math: Grade 3a Unit 2 (part 6). Singapore Math: Grade 3a Unit 2 (part 7). Singapore Math: Grade 3a Unit 2 (part 8). Singapore Math: Grade 3a Unit 2 (part 9). Singapore Math: Grade 3a Unit 2 (part 10). Singapore Math: Grade 3a Unit 2 (part 11). Singapore Math: Grade 3a, Unit 1 (part 1). Singapore Math: Grade 3a Unit 1 (part 2). Singapore Math: Grade 3a, Unit 1 (part 3). Singapore Math: Grade 3a, Unit 1 (part 4). Singapore Math: Grade 3a, Unit 1 (part 5). Singapore Math: Grade 3a, Unit 1 (part 6). Singapore Math: Grade 3a, Unit 1 (part 7). Singapore Math: Grade 3a, Unit 1 (part 8). Singapore Math: Grade 3a, Unit 1 (part 9). Singapore Math: Grade 3a Unit 2 (part 1). Singapore Math: Grade 3a Unit 2 (part 2). Singapore Math: Grade 3a Unit 2 (part 3). Singapore Math: Grade 3a Unit 2 (part 4). Singapore Math: Grade 3a Unit 2 (part 5). Singapore Math: Grade 3a Unit 2 (part 6). Singapore Math: Grade 3a Unit 2 (part 7). Singapore Math: Grade 3a Unit 2 (part 8). Singapore Math: Grade 3a Unit 2 (part 9). Singapore Math: Grade 3a Unit 2 (part 10). Singapore Math: Grade 3a Unit 2 (part 11).

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Course Format

This course has been designed for independent study. It includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:

• Lecture Videos with supporting written notes
• Recitation Videos of problem-solving tips
• Worked Examples with detailed solutions to sample problems
• Problem sets with solutions
• Exams with solutions
• Interactive Java Applets ("Mathlets") to reinforce key concepts

Content Development