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Video
Lecture videos from Gilbert Strang's course on Linear Algebra at MIT.
 Course related:
 AMA1120 Basic Mathematics II  Calculus and Linear Algebra
 Subjects:
 Mathematics and Statistics
 Keywords:
 Algebras Linear
 Resource Type:
 Video

Video
Finding the right mate is no cakewalk  but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical statistics Online dating
 Resource Type:
 Video

Video
With humor and charm, mathematician Eduardo Sáenz de Cabezón answers a question that's wracked the brains of bored students the world over: What is math for? He shows the beauty of math as the backbone of science — and shows that theorems, not diamonds, are forever. In Spanish, with English subtitles.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics
 Resource Type:
 Video

Video
Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematics  Philosophy
 Resource Type:
 Video

Video
This video playlist covers the topic of: 1. PDE 1  Introduction 2.PDE 2  Three fundamental examples 3.PDE 3  Transport equation: derivation 4.PDE 4  Transport equation: general solution 5. PDE 5  Method of characteristics 6. PDE 6  Transport with decay and nonlinear transport 7.PDE 7  Wave equation: intuition 8.PDE 8  Wave equation: derivation 9.PDE 9  Wave equation: general solution 10.PDE 10  Wave equation: d'Alembert's formula 11.PDE 11  Wave equation: d'Alembert examples 12.PDE 12  Wave equation: characteristics 13.PDE 13  Wave equation: separation of variables 14.FA 1  Fourier series introduction 15.FA 2  Computing Fourier series 16.PDE  Heat equation: intuition 17.PDE  Finite differences: introduction
 Course related:
 AMA3723 Further Mathematical Methods for Finance
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Partial
 Resource Type:
 Video

Video
In this lecture, we consider strategies for adversarial games such as chess. We discuss the minimax algorithm, and how alphabeta pruning improves its efficiency. We then examine progressive deepening, which ensures that some answer is always available.
 Course related:
 COMP4431 Artificial Intelligence
 Subjects:
 Computing and Mathematics and Statistics
 Keywords:
 Artificial intelligence
 Resource Type:
 Video

ebook
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, DiffieHellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Number theory Textbooks
 Resource Type:
 ebook

ebook
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry  the relationship between angles and distances.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Precalculus Trigonometry Textbooks
 Resource Type:
 ebook

ebook
We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don't have to be a math guru to learn from interesting, real data. (3) Data are messy, and statistical tools are imperfect. However, when you understand the strengths and weaknesses of these tools, you can use them to learn interesting things about the world. Textbook overview The chapters of this book are as follows: 1. Introduction to data. Data structures, variables, summaries, graphics, and basic data collection techniques. 2. Foundations for inference. Case studies are used to introduce the ideas of statistical inference with randomization and simulations. The content leads into the standard parametric framework, with techniques reinforced in the subsequent chapters.1 It is also possible to begin with this chapter and introduce tools from Chapter 1 as they are needed. 3. Inference for categorical data. Inference for proportions using the normal and chisquare distributions, as well as simulation and randomization techniques. 4. Inference for numerical data. Inference for one or two sample means using the t distribution, and also comparisons of many means using ANOVA. A special section for bootstrapping is provided at the end of the chapter. 5. Introduction to linear regression. An introduction to regression with two variables. Most of this chapter could be covered immediately after Chapter 1. 6. Multiple and logistic regression. An introduction to multiple regression and logistic regression for an accelerated course. Appendix A. Probability. An introduction to probability is provided as an optional reference. Exercises and additional probability content may be found in Chapter 2 of OpenIntro Statistics at openintro.org. Instructor feedback suggests that probability, if discussed, is best introduced at the very start or very end of the course.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Statistics Textbooks
 Resource Type:
 ebook

ebook
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Integral Calculus Differential calculus Textbooks
 Resource Type:
 ebook