100 Incredible Open Lectures for Math Geeks

While many math geeks out there may have been teased for their love of numbers, it’s math that makes the world go round, defining everything from the economy to how the universe itself operates. You can indulge your love of mathematics in these great lectures and lecture series. Some are meant to review the basics and others will keep you on the cutting edge of what renowned researchers are doing in the field, but all will help you expand your knowledge and spend a few hours enjoying a topic you love.

Basic Math

These lectures cover some pretty basic mathematical issues that can be a great review or help younger math lovers get a handle on a subject.

1. Metric Conversions : This lecture will teach you the formulas you need to switch between metric and English units. [SteveToner]
2. Intro to Graphing Lines : Watch this video to learn how to graph lines or to show you how to teach it to someone else. [SteveToner]
3. Review of Factoring : Forgot what factoring was all about? This downloadable video will remind you. [SteveToner]
4. LCM and Adding Rational Expressions : Continuing on with factoring, this lecture addresses the LCM and adding fractions. [SteveToner]
5. Graphing Rational Functions : Learn to create a visual representation of a rational function with a little help from this lecture. [SteveToner]
6. Sequences and Series : Check out this video to learn the mathematical basics behind series and sequences. [SteveToner]
7. Principles of Mathematics : This collection of lectures will teach you the foundations of math, so you can move ahead and learn more. [HACC]
8. Complex Numbers : Find out more or learn the basics of what makes complex numbers, well, so complex. [Sigma]
9. Math as Others See It : This lecture explains how math is used in an English hospital and in other aspects of everyday life. [Open University]
10. Structure and Randomness in Prime Numbers : Professor Terrence Tao helps students at the Australian National University and all over learn more about prime numbers in this lecture. [ANU]

Calculus

Calculus has a reputation for being hard, and while some of it surely is, these lectures show you how to conquer some pretty difficult problems as well as explain some in-depth concepts in a way you can understand.

1. Multivariable Calculus : This lecture touches on calculus topics like parametric equations and polar coordinates, among other things. [Berkeley]
2. Single Variable Calculus : Learn some of the basics of calculus like differentiation and integration of functions of one variable in this lecture. [MIT]
3. Multivariable Calculus : Check out this collection of lectures to learn about a wide range of essential calculus topics. [MIT]
4. Solving Cubic Equations : Professor Benedict H. Gross and Professor William A. Stein take a modern approach to the ancient mathematical problem of solving cubic equations in this great lecture. [Harvard]
5. The Fourier Transform and its Applications : Use this collection of lectures to master how to use the Fourier transformation. [Stanford]
6. Calculus I : Learn about limits, derivatives, integrals and much more in this free collection of lectures. [Houston]
7. Calculus and Probability : Here you’ll be able to learn how to use calculus to determine the probability of events in the life sciences. [UCLA]
8. The Calculus Lifesaver: All the Tools You Need to Excel at Calculus : Based on the book by Professor Adrian Banner, these lectures offer students a chance to approach calculus from a different perspective. [Princeton]
9. Brief Calculus : Get a succinct summary of the principles of calculus here. [ASU]
10. Honors Calculus : This free series will give you access to some of the more advanced topics in calculus. [NJIT]
11. The Fourier Series : If you’re not familiar with anything Fourier, then check out these lectures to learn more. [Open University]
12. Trigonometry for Calculus : It’s hard to master calculus without first learning the trig behind it, and these lectures will help you to do just that. [U of Idaho]

Algebra

In these lectures you’ll learn about a wide range of topics in algebra.

1. Linear Algebra : Watch the lectures here to learn about some algebraic basics like matrix theory and linear algebra. [MIT]
2. Algorithms in Algebra and Geometry, Part I : Algorithms aren’t always the easier concepts to understand but this lecture helps break it down. [MSRI]
3. Fundamentals of Algebra : Divided up into chapters, this lecture allows listeners to learn some of the basics of algebra. [Indiana University]
4. Pre-Calculus Algebra : Prepare yourself for upper-level math courses with this lecture that will give you the tools for calculus. [St. Petersburg College]
5. Intermediate Algebra : Once you’ve mastered the basics, take this course in more intermediate math topics. [HACC]
6. College Algebra : Whether you want to prepare for college or just review, this lecture will help you out. [HACC]
7. Algebraic Statistics : This conference at the MSRI has generated loads of helpful lectures on everything from permutations to integrals. [MSRI]
8. Advances in Algebra and Geometry : Make sure you’re in the loop in what’s going on in research in fields like homological algebra and birational geometry by listening to these informative lectures. [MSRI]

Geometry

These lectures cover everything from geometry basics to extremely advanced topics.

1. Connections for Women: Algebraic Geometry and Related Fields : Check out this great collection of lectures to get an idea of what women are doing in the field of algebraic geometry. [MSRI]
2. Classical Algebraic Geometry Today : Algebraic Geometry, one of the most diverse areas of mathematics, is covered in a wide range of lectures from this conference. [MSRI]
3. Combinatorial, Enumerative and Toric Geometry : These great lectures touch on topics relevant to algebraic geometry. [MSRI]
4. Algebraic Geometry : With lectures on topics like "Rationality of Gromov-Witten Varieties" this series is a must-listen for any math geek. [MSRI]
5. Symplectic and Contact Geometry and Topology : Here you’ll get a great introduction to this topic in a multi-lecture series. [MSRI]
6. Introductory Workshop: Tropical Geometry : Go to this link to learn more about the fundamentals of tropical geometry as well connected subjects like symplectic geometry, several complex variables, algebraic geometry and geometric combinatorics. [MSRI]
7. Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas : Through these lectures, you can learn more about the research being done in this field. [MSRI]
8. Geometric Evolution Equations : If you’ve ever wanted to know more about geometric flows, you’ll appreciate all the material collected in this series of lectures. [MSRI]
9. Algebraic Topology Applied in Geometry : This lecture will help you understand more about this complex topic, and includes not only the lecture itself, but notes so that you can follow along. [MSRI]
10. Arithmetic Geometry : Watch these free lectures to learn more about torsors, toric variety and rational surfaces. [Clay Mathematics Institute Summer School]
11. The Geometry of 3-Manifolds : This lecture addresses the topic of the fake 3-sphere and supplies research by a Russian mathematician that may have solved the debate over the issue. [Harvard]
12. Modern Moduli Theory : These lectures will focus on some of the most recent developments in algebraic geometry and how they can be applied to the moduli theory. [MSRI]

Other Math

These lectures covers a wide spectrum of mathematical topics from the basics of probability to the intricacies of differential equations.

1. Differential Equations : Gain a more in-depth understanding of the laws of nature in this lecture series that explores the math that lays down the foundation for them. [MIT]
2. Finite Math Online : Take a look at this lecture to learn more about working with matrices. [North Carolina State University]
3. Applied Probability : This series of lectures focuses on "modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions." [AraDigita]
4. The Arithmetic of L-functions : Check out this lecture to learn more about the applications of L-functions. [MSRI]
5. Random Matrix Theory : If you want to take your education on matrices one step further, take a look at these great lectures from big names in math. [MSRI]
6. Inverse Problems : Here you can find lectures on the topic of inverse problems from several different academics. [MSRI]
7. Combinatorial Representation Theory : CRT deals with the interplay between combinatorics and various branches of mathematics, and you can learn much more about it here. [MRSI]
8. Lie Theory : If you’ve never heard of lie theory, or the math that surrounds it, learn more from these academic lectures. [MSRI]
9. Exterior Differential Systems and the Method of Equivalence : These lectures highlight some of the academics working in this field who are focusing on things like Riemannian submersions, holonomy, almost complex manifolds, representation theory and mathematical physics. [MSRI]
10. Contact structures, dynamics and the Seiberg-Witten equations in dimension 3 : Check out these lectures to learn more about topics like homology, Seiberg-Witten and Weinstein Conjecture, and Broken Lefschetz fibrations. [MSRI]

Physics

Math forms the foundation of the science of physics and you can learn more about recent developments, the basic equations and much more in these lectures.

1. String Theory, Black Holes, and the Laws of Nature : Get a better understanding of how the universe works with new research findings on the relationship between black holes and string theory presented in these lectures. [Harvard]
2. Quantum Mechanics and the Paradoxes of Entanglement : John Conway explains how quantum mechanics works in this college-level lecture. [Princeton]
3. The Paradoxes of Relativity : Relativity has never been a particularly straightforward topic, and professor John Conway explains why this is especially true in light of new discoveries in this lecture. [Princeton]
4. Matchsticks, Scramjets, and Black Holes: Numerical Simulation Faces Reality : In this lecture, you’ll learn more about how Navy researcher Elaine Oran has made some new and interesting discoveries in the field of physics. [Princeton]
5. Einstein’s Biggest Blunder: A Cosmic Mystery Story : Einstein may have been a genius, but that doesn’t mean he was infallible, as this lecture from Lawrence Krauss explains. [Princeton]
6. Introduction to Astrophysics : Check out this lecture to learn more about Extra-Solar Planets, Black Holes, and Dark Energy. [Yale]
7. Fundamentals of Physics : If you never took physics as an undergrad, this collection of lectures will help bring you up to speed. [Yale]
8. Physics I: Classical Mechanics : In this lecture you’ll learn the basics of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. [MIT]
9. Physics II: Electricity and Magnetism : These lectures continue the theme begun in the first of the series, except learners will now get a chance to find out more about electricity and magnetism. [MIT]
10. Physics III: Vibrations and Waves : Listen to these lectures to get an education on the physics of vibrations and waves. [MIT]
11. Black Holes in Relativity : These lectures explore the often complicated math that lies behind understanding relativity and its application to black holes. [MSRI]
12. A Window into Zeta and Modular Physics : Visit this site to find a great collection of lectures on Riemann zeta function and hot topics like black holes, relativity and string theory. [MSRI]
13. Dynamical Systems and Chaos : Use these lectures to learn more about the origins of theories on chaos, views of the universe and the numerical analysis that followed. [Texas A&M]

Engineering

Get a better idea of the math behind engineering of all kinds with these great lectures.

1. The Fluid World: Flows, Films and Foams : Professor Howard A. Stone explains fluid dynamics in this series of lectures. [Harvard]
2. Computational Science and Engineering I : Use these lectures to review linear algebra, differential equations, boundary-value problems and more. [MIT]
3. Mathematical Methods for Engineers II : Watch these lectures to learn about topics like numerical methods; initial-value problems; network flows; and optimization. [MIT]
4. Introduction to Quantum Computing : Have no idea what quantum computing is all about? Learn more in this lecture and accompanying materials. [MSRI]
5. Modern Perspectives in Applied Mathematics : These lectures will touch upon stochastic and multi-scale modeling and how they are applied in science and engineering. [MSRI]
6. Stochastic Dynamical Systems and Control : Check out these lectures to learn more about these issues that affect many aspects of engineering and computing. [MSRI]
7. Introduction to Linear Dynamical Systems : These lectures will teach you about computational issues like circuits, signal processing, communications, and control systems. [Stanford]
8. Convex Optimization I : The first part in a series, this lecture will help you learn to solve some of the more complex problems that arise in engineering. [Stanford]
9. Convex Optimization II : Part two of this series will educate you on topics like subgradients, cutting-planes, and ellipsoid methods.[Stanford]

Business and Economics

Watch or listen to these lectures to learn something new about statistics, economics, or the basic mathematical principles of the financial world.

1. Beyond Freakonomics: New Musings on the Economics of Everyday Life : Here you’ll get some insights into how economics translates into smaller, everyday situations. [Princeton]
2. Mathematics of Finance : Learn the absolute basics of things like interest, financial decision making and more from these video lectures. [North Carolina State University]
3. Economic Games and Mechanisms to Address Climate Change : These lectures examine the theoretical and applied models of bargaining, with special attention to business decisions like CO2 emissions caps. [MSRI]
4. Introduction to Statistics : If you’ve never taken much in the way of statistics before, these lectures will get you started. [Berkeley]
5. Statistics with Microsoft Excel : Learn how to use Microsoft Excel as a helpful tool in modeling and organizing information for statistical analysis. [microbiologybytes]
6. Elementary Statistics : This lecture will teach you the fundamentals of statistics and what the results mean when you’re analyzing large amounts of data. [Sofia]

Special Topics

1. Escher and the Droste Effect : The Droste Effect is what makes images look as if they go on forever, and this lecture will allow you to learn more about how this works mathematically and visually. [Princeton]
2. Fermat’s Last Theorem – The Theorem and Its Proof: An Exploration of Issues and Ideas : Robert Osserman, Lenore Blum, Ken Ribet, John Conway, and Lee Dembart all talk in this lecture on how they went about proving Fermat’s theorem. [MSRI]
3. Sage Days: Algebraic Geometry : The lectures found here aren’t just about doing algebraic geometry but about how to use computer programs, namely Sage, to do so. [MSRI]
4. Coding Theory : Hear from some experts in the field about the many complications that come up in computer coding and digital communications. [MSRI]
5. Experimental Mathematics : If you want to learn more about the cutting edge of mathematics, check out these lectures from the MSRI on "Numerical Intergration Techniques with Rational Landen Transformations" and "Structure of p-adic valuations of Stirling numbers." [MSRI]
6. Modular Forms and Arithmetic : These lectures are not for math newbies and offer some ways that modular forms can be applied in arithmetic. [MSRI]
7. Discrete Rigidity Phenomena in Additive Combinatorics : This series of lectures deals with "environments in which rigid structural information can be deduced from rather soft combinatorial hypotheses." [MSRI]
8. Mathematics of Markov Chain Monte Carlo : Use this lecture as a chance to learn more about the math behind this card game. [MSRI]

Math and Science

Learn about the relationship between math and science in these lectures.

1. Mathematical aspects of computational biology : Learn more about the math that goes behind organizing the large amount of biological data being gathered, especially in the fields of genomic research, from this series of lectures. [MSRI]
2. Mathematical Genomics : These lectures will help you learn more about bringing together the field of genetic research and the math that aids in its analysis and use. [MSRI]
3. Math in Nature and Art : Learn just what role math plays in nature and art and the importance of fractals from this lecture. [Open University]
4. Sounds Harmonious : This lecture will educate you on the mathematical aspects of hearing and music. [Open University]
5. The Rainbow Analyzed : Check out this lecture to learn the math and physics behind why rainbows look like they do. [Open University]
6. Mathematics of Visual Analysis : Here you can learn about the role math plays in analyzing large amounts of information for science and commerce. [MSRI]

Teaching

These lectures will help you learn to better teach math to others.

1. Teaching Undergraduates Mathematics : This lecture series will allow professors, and upper level math students, to learn what it takes to teach students at the college level more effectively. [MSRI]
2. Critical Issues in Education Workshop: Teaching and Learning Algebra : Get some helpful tips and tools to improve your skills at teaching algebra in these lectures. [MSRI]
3. Using Partnerships to Strengthen Elementary Mathematics Teacher Education : Listen to these lectures on building partnerships that can help improve US math education programs. [MSRI]
4. Critical Issues in Education: Teaching Teachers Mathematics : Many lectures focus on teaching students, but what about teaching teachers? If you plan on teaching math these lectures are a good place to start learning about math education even after graduation. [MSRI]
5. Fun with Mathematics: Some Thoughts from Seven Decades : Can math be fun? This lecture addresses a number of mathematical teaching and learning issues. [MSRI]
6. Great Circles 2009 : These lectures are meant to inspire teachers, students and scholars alike to spread math learning circles to their own communities. [MSRI]