Mathematics

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MIT OCW
free course
Real Analysis
Prof. Tobias Colding
This course gives an introduction to analysis, and the goal is twofold:          ...
Mathematics Science & Math
intermediate
MIT OCW
free course
Classical Mechanics
Prof. Deepto Chakrabarty
This first course in the physics curriculum introduces classical mechanics. Historically, a set of core...
Physics Science & Math
intermediate
MIT OCW
free course
Matrix Calculus for Machine Learning and Beyond
Prof. Alan Edelman
We all know that calculus courses such as 18.01 Single Variable Calculus and 18.02 Multivariable Calculus cover...
Mathematics Science & Math
intermediate
MIT OCW
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Linear Algebra
Prof. Gilbert Strang
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Differential Equations
Dr. Jeremy Orloff
This course, taught to students in MIT’s Experimental Study Group, is equivalent to the Mathematics Department’s...
Mathematics Science & Math
intermediate
MIT OCW
free course
Calculus I: Single Variable Calculus
Prof. David Jerison
Master the calculus of derivatives, integrals, coordinate systems, and infinite series. In this three-part series...
Mathematics Science & Math
intermediate
MIT OCW
free course
Multivariable Calculus
Prof. Denis Auroux
This course covers differential, integral and vector calculus for functions of more than one variable. These...
Mathematics Science & Math
intermediate
MIT OCW
free course
Principles of Discrete Applied Mathematics
Prof. Ankur Moitra
This course will teach you illustrative topics in discrete applied mathematics, including counting, generating...
Mathematics Communication Social Sciences
intermediate
MIT OCW
free course
Differential Geometry
Prof. Paul Seidel
This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still...
Mathematics Science & Math
intermediate
MIT OCW
free course
Physics I: Classical Mechanics
Prof. Adam Burgasser
This class is an introduction to classical mechanics for students who are comfortable with calculus. The main topics...
Physics Science & Math
intermediate
MIT OCW
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Single Variable Calculus
Prof. David Jerison
This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief...
Mathematics Science & Math
intermediate
MIT OCW
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Introduction to Topology
Prof. James Munkres
This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with...
Mathematics Science & Math
intermediate
MIT OCW
free course
Organic Chemistry I
Dr. Kimberly Berkowski
This subject deals primarily with the basic principles to understand the structure and reactivity of organic...
Chemistry Science & Math
intermediate
MIT OCW
free course
Physical Chemistry
Prof. Robert Field
This course is an introduction to quantum mechanics for use by chemists. Topics include particles and waves, wave...
Chemistry Science & Math
intermediate
MIT OCW
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Modern Algebra
Prof. James McKernan
This undergraduate course focuses on traditional algebra topics that have found greatest application in science and...
Mathematics Science & Math
intermediate
MIT OCW
free course
Introduction to Functional Analysis
Dr. Casey Rodriguez
Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no...
Mathematics Science & Math
intermediate
MIT OCW
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Fundamentals of Biology
Prof. Eric Lander
Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and...
Biology Science & Math
intermediate
MIT OCW
free course
Principles of Chemical Science
Prof. Catherine Drennan
This course provides an introduction to the chemistry of biological, inorganic, and organic molecules. The emphasis...
Chemistry Science & Math
intermediate
MIT OCW
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Biological Chemistry I
Prof. John Essigmann
This course examines the chemical and physical properties of the cell and its building blocks, with special emphasis...
Biology Science & Math
intermediate
MIT OCW
free course
Physics III: Vibrations and Waves
Prof. Yen-Jie Lee
Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant...
Physics Science & Math
intermediate
MIT OCW
free course
Mathematical Problem Solving (Putnam Seminar)
Prof. Yufei Zhao
This course is a seminar intended for undergraduate students who enjoy solving challenging mathematical problems,...
Science & Math Mathematics
intermediate
MIT OCW
free course
Engineering Math: Differential Equations and Linear Algebra
Prof. Daniel Frey
This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An...
Engineering Mathematics Mechanical Engineering
intermediate
MIT OCW
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The Early Universe
Prof. Alan Guth
The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the...
Physics Science & Math
intermediate
MIT OCW
free course
Physics II: Electricity and Magnetism
Prof. Gabriella Sciolla
Course 8.022 is one of several second-term freshman physics courses offered at MIT. It is geared towards students...
Physics Science & Math
intermediate
MIT OCW
free course
Introduction to Partial Differential Equations
Prof. Jared Speck
This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It...
Mathematics Science & Math
intermediate
MIT OCW
free course
Electromagnetism II
Prof. Alan Guth
This course is the second in a series on Electromagnetism beginning with Electromagnetism I (8.02 or 8.022). It is a...
Physics Science & Math
intermediate
MIT OCW
free course
Computational Science and Engineering I
Dr. Chengzhao (Richard) Zhang
This course provides the fundamental computational toolbox for solving science and engineering problems. Topics...
Engineering Mathematics Systems Engineering
intermediate
MIT OCW
free course
Theory of Numbers
Prof. Abhinav Kumar
This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include...
Mathematics Science & Math
intermediate
MIT OCW
free course
Modern Astrophysics
Prof. Paul Schechter
This course explores the applications of physics (Newtonian, statistical, and quantum mechanics) to fundamental...
Physics Science & Math
intermediate
MIT OCW
free course
Algebra I
Prof. Michael Artin
This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Introduction to Statistical Method in Economics
Herman Bennett
This course is a self-contained introduction to statistics with economic applications. Elements of probability...
Mathematics Economics Social Sciences
intermediate
MIT OCW
free course
Introduction to Biology
Dr. Claudette Gardel
The MIT Biology Department core courses, 7.012, 7.013, and 7.014, all cover the same core material, which includes...
Biology Science & Math
intermediate
MIT OCW
free course
Calculus with Applications
Daniel Kleitman
This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and...
Mathematics Science & Math
intermediate
MIT OCW
free course
Introduction to Analysis
Prof. Arthur Mattuck
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Organic Chemistry II
Dr. Sarah Tabacco
This intermediate organic chemistry course focuses on the methods used to identify the structure of organic...
Chemistry Science & Math
intermediate
MIT OCW
free course
Calculus with Theory
Christine Breiner
18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more...
Mathematics Science & Math
intermediate
MIT OCW
free course
Fundamentals of Experimental Molecular Biology
Dr. Eric Chu
7.002 is a laboratory course that teaches fundamental skills for performing biological research. Through experiments...
Biology Science & Math
intermediate
MIT OCW
free course
Classical Mechanics II
Prof. Matthew Evans
This undergraduate course is a broad, theoretical treatment of classical mechanics, useful in its own right for...
Physics Science & Math
intermediate
MIT OCW
free course
Introduction to Statistical Methods in Economics
Konrad Menzel
This course will provide a solid foundation in probability and statistics for economists and other social...
Mathematics Economics Social Sciences
intermediate
MIT OCW
free course
Combinatorial Analysis
Prof. Richard Stanley
This course analyzes combinatorial problems and methods for their solution. Topics include: enumeration, generating...
Mathematics Science & Math
intermediate
MIT OCW
free course
Advanced Organic Chemistry
Prof. Mohammad Movassaghi
This course deals with the application of structure and theory to the study of organic reaction mechanisms:...
Chemistry Science & Math
intermediate
MIT OCW
free course
Statistical Physics I
Prof. Thomas Greytak
This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are...
Physics Mathematics Science & Math
intermediate
MIT OCW
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Relativity
Prof. Max Tegmark
This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year....
Physics Science & Math
intermediate
MIT OCW
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7.28x Molecular Biology
Prof. Stephen P. Bell
This course is an in-depth adventure through the molecular mechanisms that control the maintenance, expression, and...
Biology Science & Math
intermediate
MIT OCW
free course
String Theory for Undergraduates
Prof. Barton Zwiebach
This course introduces string theory to undergraduate and is based upon Prof. Zwiebach’s textbook entitled A First...
Physics Science & Math
intermediate
MIT OCW
free course
Linear Partial Differential Equations: Analysis and Numerics
Prof. Steven G. Johnson
This course provides students with the basic analytical and computational tools of linear partial differential...
Mathematics Science & Math
intermediate
MIT OCW
free course
Physics Demonstration Videos
MIT Department of Physics Technical Services Group
The Technical Services Group at MIT’s Department of Physics provides technical and teaching support for...
Physics Science & Math
intermediate
MIT OCW
free course
Algebraic Combinatorics
Prof. Alexander Postnikov
This course covers the applications of algebra to combinatorics. Topics include enumeration methods, permutations,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Biological Chemistry II
Prof. Joanne Stubbe
This course is an advanced treatment of biochemical mechanisms that underlie biological processes. Topics include...
Biology Chemistry Science & Math
intermediate
MIT OCW
free course
Multivariable Calculus with Theory
Christine Breiner
This course is a continuation of 18.014 Calculus with Theory. It covers the same material as 18.02 Multivariable...
Mathematics Science & Math
intermediate
MIT OCW
free course
Biochemical Engineering
Prof. Kristala L. Jones Prather
This course focuses on the interaction of chemical engineering, biochemistry, and microbiology. Mathematical...
Biology Chemical Engineering Engineering
intermediate
MIT OCW
free course
Physics I: Classical Mechanics with an Experimental Focus
Prof. Kate Scholberg
Physics I is a first-year physics course which introduces students to classical mechanics. This course has a...
Physics Science & Math
intermediate
MIT OCW
free course
Cellular Neurobiology
Prof. Troy Littleton
This course serves as an introduction to the structure and function of the nervous system. Emphasis is placed on the...
Biology Cognitive Science Science & Math
intermediate
MIT OCW
free course
Analysis I
Prof. Katrin Wehrheim
Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Principles of Applied Mathematics
Prof. Rodolfo Rosales
18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Kitchen Chemistry
Dr. Patricia Christie
This seminar is designed to be an experimental and hands-on approach to applied chemistry (as seen in cooking)....
Chemistry Science & Math
intermediate
MIT OCW
free course
Applied Category Theory
Dr. David I. Spivak
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The...
Mathematics Science & Math
intermediate
MIT OCW
free course
Chemical and Biological Reaction Engineering
Prof. K. Dane Wittrup
This course applies the concepts of reaction rate, stoichiometry and equilibrium to the analysis of chemical and...
Biological Engineering Chemistry Chemical Engineering
intermediate
MIT OCW
free course
Introduction to Special Relativity
Prof. Markus Klute
The theory of special relativity, originally proposed by Albert Einstein in his famous 1905 paper, has had profound...
Physics Science & Math
intermediate
MIT OCW
free course
Calculus Open Textbook
Prof. Gilbert Strang
First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for...
Mathematics Science & Math
intermediate
MIT OCW
free course
Linear Algebra - Communications Intensive
Andrew Brooke-Taylor
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of...
Mathematics Literature Humanities
intermediate
MIT OCW
free course
Complex Variables with Applications
Dr. Jeremy Orloff
Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It...
Mathematics Science & Math
intermediate
MIT OCW
free course
Multivariable Calculus Recitation Notes
Dr. Evan Chen
These lecture notes and exercises (with solutions) cover MIT’s multivariable calculus sequence as taught in Fall...
Mathematics Science & Math
intermediate
MIT OCW
free course
Classical Mechanics III
Prof. Iain Stewart
This course covers Lagrangian and Hamiltonian mechanics, systems with constraints, rigid body dynamics, vibrations,...
Physics Science & Math
intermediate
MIT OCW
free course
Analysis II
Prof. Victor Guillemin
This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half...
Mathematics Science & Math
intermediate
MIT OCW
free course
Calculus of Several Variables
Prof. James McKernan
This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on...
Mathematics Science & Math
intermediate
MIT OCW
free course
Integrated Chemical Engineering I
Dr. Barry S. Johnston
This course uses reaction kinetics, batch reactor analysis, batch distillation, batch operations scheduling, safety...
Chemistry Chemical Engineering Engineering
intermediate
MIT OCW
free course
Systems Microbiology
Prof. David Schauer
This course covers introductory microbiology from a systems perspective, considering microbial diversity, population...
Biology Biological Engineering Engineering
intermediate
MIT OCW
free course
Highlights of Calculus
Prof. Gilbert Strang
Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is...
Mathematics Science & Math
intermediate
MIT OCW
free course
Fourier Analysis
Prof. David Jerison
This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory...
Mathematics Science & Math
intermediate
MIT OCW
free course
Electricity and Magnetism
Bruce Knuteson
This freshman-level course is the second semester of introductory physics. The focus is on electricity and...
Physics Science & Math
intermediate
MIT OCW
free course
Transport Processes
Prof. Clark Colton
Principles of heat and mass transfer. Steady and transient conduction and diffusion. Radiative heat transfer....
Physics Chemical Engineering Engineering
intermediate
MIT OCW
free course
Geometry and Topology in the Plane
Prof. Paul Seidel
This course introduces students to selected aspects of geometry and topology, using concepts that can be visualized...
Mathematics Science & Math
intermediate
MIT OCW
free course
Separation Processes
Dr. William Dalzell
This course covers the general principles of separation by equilibrium and rate processes. Topics include staged...
Chemistry Chemical Engineering Engineering
intermediate
MIT OCW
free course
A Vision of Linear Algebra
Prof. Gilbert Strang
This collection of videos presents Professor Strang’s updated vision of how linear algebra could be taught. It...
Mathematics Science & Math
intermediate
MIT OCW
free course
Neural Basis of Learning and Memory
Prof. Matt Wilson
This course highlights the interplay between cellular and molecular storage mechanisms and the cognitive...
Biology Cognitive Science Science & Math
intermediate
MIT OCW
free course
Laboratory Fundamentals in Biological Engineering
Prof. Drew Endy
This course introduces experimental biochemical and molecular techniques from a quantitative engineering...
Systems Engineering Biology Biological Engineering
intermediate
MIT OCW
free course
Exploring Black Holes: General Relativity & Astrophysics
Prof. Edmund Bertschinger
Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity,...
Physics Science & Math
intermediate
MIT OCW
free course
Algebra II
Prof. Michael Artin
This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Linear Partial Differential Equations
Dr. Matthew Hancock
This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Laboratory Chemistry
Dr. John J. Dolhun
This course introduces experimental chemistry for students who are not majoring in chemistry. The course covers...
Chemistry Science & Math
intermediate
MIT OCW
free course
Physics II: Electricity & Magnetism with an Experimental Focus
Prof. Gunther M. Roland
This course is an introduction to electromagnetism and electrostatics. Topics include: electric charge, Coulomb’s...
Physics Science & Math
intermediate
MIT OCW
free course
Algebra II Student Notes
Algebra II is the second semester of a year-long introduction to modern algebra. The course focuses on group...
Mathematics Science & Math
intermediate
MIT OCW
free course
Experimental Physics I & II "Junior Lab"
Physics Department Faculty, Lecturers, and Technical Staff
Junior Lab consists of two undergraduate courses in experimental physics. The course sequence is usually taken by...
Physics Science & Math
intermediate
MIT OCW
free course
Animal Behavior
Prof. Gerald E. Schneider
The introductory topics will cover various approaches to the study of animals and their behavior. Key concepts in...
Biology Cognitive Science Science & Math
intermediate
MIT OCW
free course
Analysis of Biomolecular and Cellular Systems
Prof. Ernest Fraenkel
This course focuses on computational and experimental analysis of biological systems across a hierarchy of scales,...
Engineering Biology Biological Engineering
intermediate
MIT OCW
free course
Applied Molecular Biology Lab
Dr. Vanessa Cheung
7.003 is an experimental biology course. You will spend most of your time in the teaching laboratory practicing...
Biology Science & Math
intermediate
MIT OCW
free course
Separation Processes for Biochemical Products
Prof. Charles Cooney
This course serves as an introduction to the fundamental principles of separation operations for the recovery of...
Biology Chemistry Chemical Engineering
intermediate
MIT OCW
free course
Introduction to Organic Synthesis Laboratory
Prof. Rick Danheiser
This course, which spans a third of a semester, provides students with experience using techniques employed in...
Engineering Chemistry Chemical Engineering
intermediate
MIT OCW
free course
Functions of a Complex Variable
Prof. Sigurdur Helgason
This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis....
Mathematics Science & Math
intermediate
MIT OCW
free course
Uncertainty in Engineering
Prof. Daniele Veneziano
This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course...
Mathematics Engineering Civil Engineering
intermediate
MIT OCW
free course
Introduction to Representation Theory
Prof. Pavel Etingof
The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie...
Mathematics Science & Math
intermediate
MIT OCW
free course
Cognitive Processes
Prof. Mary C. Potter
This undergraduate course is designed to introduce students to cognitive processes. The broad range of topics covers...
Cognitive Science Science & Math
intermediate
MIT OCW
free course
Honors Differential Equations
Prof. Jason Starr
This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Calculus Revisited: Single Variable Calculus
Prof. Herbert Gross
Calculus Revisited is a series of videos and related resources that covers the materials normally found in a...
Mathematics Science & Math
intermediate
MIT OCW
free course
Developmental Biology
Prof. Hazel Sive
This graduate and advanced undergraduate level lecture and literature discussion course covers the current...
Biology Science & Math
intermediate
MIT OCW
free course
Chemistry Laboratory Techniques
Dr. John J. Dolhun
This course is an intensive introduction to the techniques of experimental chemistry and gives first year students...
Chemistry Science & Math
intermediate
MIT OCW
free course
Introduction to Experimental Chemistry
Prof. Keith Nelson
This course is the first part of a modular sequence of increasingly sophisticated (and challenging) laboratory...
Chemistry Science & Math
intermediate
MIT OCW
free course
Introduction to Metric Spaces
Paige Bright
This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous...
Mathematics Science & Math
intermediate
MIT OCW
free course
Calculus Revisited: Multivariable Calculus
Prof. Herbert Gross
Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman-...
Mathematics Science & Math
intermediate
MIT OCW
free course
Integrated Chemical Engineering Topics I: Process Control by Design
Dr. Barry S. Johnston
In the ICE-Topics courses, various chemical engineering problems are presented and analyzed in an industrial...
Environmental Engineering Chemistry Chemical Engineering
intermediate
MIT OCW
free course
Undergraduate Seminar in Discrete Mathematics
Dr. Omer Tamuz
This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general....
Mathematics Science & Math
intermediate
MIT OCW
free course
The Art of Counting
Prof. Richard Stanley
The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance,...
Mathematics Science & Math
intermediate
MIT OCW
free course
Statistical Physics II
Prof. Xiao-Gang Wen
This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical,...
Physics Mathematics Science & Math
intermediate
MIT OCW
free course
Introduction to Arithmetic Geometry
Andrew V. Sutherland
This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry...
Mathematics Science & Math
intermediate
MIT OCW
free course
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra
Prof. Herbert Gross
Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman-...
Mathematics Science & Math
intermediate
MIT OCW
free course
Experimental Molecular Neurobiology
Prof. Carlos Lois
Designed for students without previous experience in techniques of cellular and molecular biology, this class...
Biology Cognitive Science Science & Math
intermediate
MIT OCW
free course
Physics of Solids I
Prof. Xiao-Gang Wen
This course offers an introduction to the basic concepts of the quantum theory of solids.
Physics Science & Math
intermediate
MIT OCW
free course
Drugs and the Brain
Zak Fallows
This class is a multidisciplinary introduction to pharmacology, neurotransmitters, drug mechanisms, and brain...
Biology Science & Math
intermediate
MIT OCW
free course
Vibrations and Waves Problem Solving
Prof. Wit Busza
8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01...
Physics Science & Math
intermediate
MIT OCW
free course
System Functions and the Laplace Transform
Dr. Philip Pearce
This half-semester course studies basic continuous control theory as well as representation of functions in the...
Mathematics Science & Math
intermediate
MIT OCW
free course
Digital Lab Techniques Manual
Dr. Kimberly Berkowski
The “Digital Lab Techniques Manual” is a series of videos designed to help you prepare for your chemistry laboratory...
Chemistry Science & Math
intermediate
MIT OCW
free course
Calculus for Beginners and Artists
Daniel Kleitman
This online textbook provides an overview of Calculus in clear, easy to understand language designed for the...
Science & Math Mathematics
intermediate
MIT OCW
free course
Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry
Prof. Steven Kleiman
In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject...
Mathematics Science & Math
intermediate