Logic for Computer Science: Foundations of Automatic Theorem Proving
This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. The book is self contained, and the level corresponds to senior undergraduates and first year graduate students. However,
Missing Angle Puzzles
This lesson lays some of the ground work for eventually writing two column proofs. In the lesson students use known geometric facts to solve for missing angles. Students are asked to identify the key concepts required for the solution and to record the a path for finding the measure of a particular angle. Key concepts include the sum of the measures of the interior angles of a triangle and quadrilateral, parallel line relationships, and what can and cannot be assumed from a drawing.
Introduction to compact operators
The aim of this session is to cover the basic theory of compact linear operators on Banach spaces. This includes definitions and statements of the background and main results, with illustrative examples and some proofs. Target audience: This material is accessible to anyone who has a basic knowledge of metric space topology, and who knows what a bounded linear operator on a Banach space is. It is most likely to be suitable for postgraduate students or final year undergraduates.
When I started teaching this subject I found three kinds of texts. There were applications books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs and know how to answer the homework questions having seen only one or two examples. And, there were books that spend a good part of the semester multiplying matrices and computing determinants and then suddenly change level to wo
Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i
Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey
Existential Graphs is a Web resource offering an introduction to the existential graphs system of logic, originally developed about a century ago by American philosopher Charles S. Pierce. The system offers a way of formalising and analysing logical arguments, including methods for testing proofs, but unlike more conventional formalisation systems, it adopts a graphical approach. Although the method will be unfamiliar to many students of logic, Pierce claimed that it was easier to use than tradi
18.014 Calculus with Theory I (MIT)
18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary f
6.876J Advanced Topics in Cryptography (MIT)
The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security.
18.314 Combinatorial Analysis (MIT)
This course analyzes combinatorial problems and methods for their solution. Prior experience with abstraction and proofs is helpful. Topics include: Enumeration, generating functions, recurrence relations, construction of bijections, introduction to graph theory, network algorithms and, extremal combinatorics.
6.042J Mathematics for Computer Science (MIT)
This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics f
Green still big at auto show
The Detroit Auto Show kicks off with a return by Porsche and a focus on "green" from Toyota, Ford and all the big players, as the technology moves beyond a futuristic concept to reality.
18.704 Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometr
In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.
18.312 Algebraic Combinatorics (MIT)
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
Lugosi teaches math - convergence of series
Béla Lugosi teaches advanced mathematical concepts in this video. This is part of the last lecture of his series. He begins this lecture by talking about the Weierstrauss M-Test and talking about how a series or sequence of sums converges. In his lecture he provides the steps for this test, and proofs as well. A great video for advanced math learners. (Calculus and Calculus II students).
How to Solve Geometry Proofs
Excellent video from Jimmy Chang, who has a master's degree in math and has been a math teacher at St. Pete College for more than eight years. Mr. Chang explains what geometry proofs are and their importance.
Vector Calculus: More on Green's Theorem
This is the second lecture by Dr. Chris Tisdell on Green's theorem and it's use. In this lecture he explores some interesting applications of Green's theorem and presents several examples. Also, some proofs are discussed.
18.024 Calculus with Theory II (MIT)
This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techn
18.06CI Linear Algebra - Communications Intensive (MIT)
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.
6.080 Great Ideas in Theoretical Computer Science (MIT)
This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity—with Euclid's algorithm and other ancient examples of computational thinking—the course will progress rapidly through propositional logic, Turing machines and computability, fin