The notes cover introduction to proofs, axioms of fields, complex numbers, some topology, and limits, continuity, derivatives, integrals, sequences and series. For teaching proof writing, many proofs contain in red color parts of proofs that should not be written down but should be thought.
This series of 5 videos will provide an introduction to geometric calculus for those who know some vector calculus. It is based on my textbook "Vector and Ge...
Mathematics as a Non-Superstition. Eleven math courses (in the playlists), from high school (precalculus) to early graduate school (functional analysis), taught in such a way that the student should be able to defend (almost) all statements against objection.
Playlist List (sorted by last added):
Course 4: Linear Algebra
Course 3: Calculus II (US)
Course 2: Calculus I (Another extra)
Course 7: Principles of Mathematical Analysis
Course 9: Basic Functional and Harmonic Analysis
Course 8: Fourier Analysis
Course 8: Complex Analysis
Course 6: Introduction to Analysis
Course 5: Differential Equations
Course 4: Multivariable Calculus
Course 3: Calculus II
Course 2: Calculus I
Course 1: Precalculus
Principles of Mathematical Analysis (based on Rudin's book of that name, Chapters 1, 2, 4, 5, 3, 7). (Prerequisites: some familiarity with theoretical mathem...
An introduction to theoretical mathematics via the basic concepts of analysis: fields, the real numbers, least upper bounds, the limit, sequences, Cauchy seq...
I present the existence and uniqueness theorem for first-order ordinary differential equations. For an introduction to differential equations, see my video: ...
This video answers the following questions: What are differential equations? What does it mean if a function is a solution of a differential equation? Why ar...
This is an excellent tool to learn how to solve math problems. Students type the story problem. And the software is giving the answer in step-by-step solution. All the steps and explanations help students to understand how to look at a problem, see the key words, and reach to solutions. I think this can help parents to help their children in math as well.
On November 11, 1675, German mathematician and polymath Gottfried Wilhelm Leibniz demonstrates integral calculus for the first time to find the area under the graph of y = ƒ(x).
On August 21, 1789, French mathematician Augustin-Louis Cauchy was born. He is considered one of the greatest mathematicians during the nineteenth century. There are 16 concepts and theorems named for Cauchy, more than for any other mathematician. Cauchy was one of the most prolific mathematicians of all times. Cauchy wrote 789 papers, a quantity exceeded only by Euler and Cayley, which brought precision and rigor to mathematics.
This interactive tutorial will teach you how to use the sequent calculus, a simple set of rules with which you can use to show the truth of statements in first order logic. It is geared towards anyone with some background in writing software for computers, with knowledge of basic boolean logic.
Abstract. Join patterns are an attractive declarative way to synchronize both threads and asynchronous distributed computations. We explore joins in the context of extensible pattern matching that recently appeared in languages such as F# and Scala. Our implementation supports join patterns with multiple synchronous events, and guards. Furthermore, we integrated joins into an existing actor-based concurrency framework. It enables join patterns to be used in the context of more advanced synchronization modes, such as future-type message sending and token-passing continuations.
"I am a professor of computer science in Orléans (teaching: IUT, UFR Sciences - research: LIFO). My general interests are in programming language design and implementation, constraint programming, and computational linguistics."