Online courses directory (391)

Provides a firm grounding in the foundations of probability and statistics, the course focuses on real examples from the medical literature and popular press

Provides a firm grounding in the foundations of probability and statistics, the course focuses on real examples from the medical literature and popular press.

Statistics One is a comprehensive yet friendly introduction to statistics.

This free online course is the first of our Upper-Secondary Mathematics suite of courses. It covers mathematical analysis, including univariate statistics and data, bivariate statistics, correlation, regression, residual analysis, non-linear data, and seasonal movements. This course is suitable for students of maths, especially those preparing for examinations. It is also suitable for those looking to refresh their knowledge of Mathematics. <br />

This course is an introduction to the key ideas and principles of the collection, display, and analysis of data to guide you in making valid and appropriate conclusions about the world.

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

在社会学、心理学、教育学、经济学、管理学、市场学等研究领域的数据分析中，结构方程建模是当前最前沿的统计方法中应用最广、研究最多的一个。它包含了方差分析、回归分析、路径分析和因子分析，弥补了传统回归分析和因子分析的不足，可以分析多因多果的联系、潜变量的关系，还可以处理多水平数据和纵向数据，是非常重要的多元数据分析工具。本课程系统地介绍结构方程模型和LISREL软件的应用，内容包括：结构方程分析（包括验证性因子分析）的基本概念、统计原理、在社会科学研究中的应用、常用模型及其LISREL程序、结果的解释和模型评价。学员应具备基本的统计知识（如：标准差、t-检验、相关系数），理解回归分析和因子分析的概念。 注：本课程配套教材为《结构方程模型及其应用》（以LISREL软件为例）。

The Statics of Everyday Objects is a course about how structures react to forces exerted on them while remaining unmoved.

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 2^n-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.

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 graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

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 covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

The goal of this course is to describe some of the tools which enter into the proof of Sullivan's conjecture.

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor.

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.