| Learning computer science has to do with a lot more than just codes and programming languages. When you were in school your teachers would have told you how all subjects are related. Well, these tutorials will show you how computer science is related to mathematics. There are also tutorials on other topics related to computer science. Enjoy! |  |
This is a cheat sheet containing computer related topics such as Boolean logic, logical quantifiers, set theory, number theory, computational complexity, searching, sorting and series.
Introduction: It will cover designing Turing Machines to accept languages, as well the concept of acceptance vs. decidability. By the conclusion of this tutorial, the reader will begin to see both the power and limitations of computing models.
Introduction: This tutorial will explore languages that Turing Machines can (and cannot) decide and accept. In essence, it takes the concepts from the last tutorials and begins to actually explore the limits of Turing Machines. Familiarity with Formal Languages is assumed.
Introduction: In modern computability theory, there exist numerous models of computation, such as Lambda Calculus, Von Neumann Computers, and Turing Machines. Each of these, while vastly different on the surface, are equivalent models of computation. That is, anything each of these models can (or cannot) compute can (or cannot) also be computed by any of these other models. The Turing Machine is considered the standard model of computation. This tutorial will explore Turing Machines and their uses in determining the limits and power of computers. Some familiarity with Formal Languages is assumed.
Introduction: This tutorial will introduce the adjacency matrix, as well as spectral graph theory. For those familiar with Linear Algebra, the spectrum of a matrix denotes its eigenvalues and their algebraic multiplicities. Spectral Graph Theory deals with the eigenvalues and eigenvectors associated with the Adjacency and Laplacian matrices. Note that the Laplacian matrix will not be discussed in this tutorial.
In this tutorial you will learn about the different structures that are used to represent graphs. These include adjacency matrices, incidence matrices, distance matrices, incidence lists and adjacency lists.
This is an introduction to the Algebraic Graph Theory (AGT). It covers vector spaces related to edges, vertices, cuts and cycles. It discussed AGT with respect to Linear Algebra.
In this tutorial you will learn about limits, matrix determinants and application of limits with dynamical systems.
This is the first in a series of tutorial that will teach you all about Linear Algebra. Wondering why mathematics is being taught? Because Linear Algebra is very closely related to computer science and programming.
This is part 2 of the Linear Algebra tutorial.
This is part 3 of the Linear Algebra tutorial.
This is part 4 of the Linear Algebra tutorial.
This is part 5 of the Linear Algebra tutorial.
This is part 6 of the Linear Algebra tutorial.
This is part 7 of the above tutorial. It deals with the Eigen Theory.
In this tutorial you will learn about basic algorithm analysis with emphasis on the time complexity of algorithms. It includes tools like Big-O, Big-Thera and Big-Omega.
This tutorial is an introduction to proofs using math induction along with Big-O proofs. Math inductions are commonly used in order to prove theorems in computer science.
