Apr 17, 2020 the mathematics department at mit is a world leader in pure and applied mathematical research and education. This fall i will be teaching the required discrete math for cs course to about fifty students at the university of south carolina. Mit mathematics courses available online and for free. Find materials for this course in the pages linked along the left. Browse through, download and use materials from more than 2,450 mit oncampus courses, all available under a creative commons license for open sharing. Even the structure of the book does nothing to help explain it there is no cohesion. A function f from a to b is called onto, or surjective, if and only if for every element b. This calendar provides links to lecture slides, accompanying lecture notes, class problems, course. Tom leighton, marten van dijk this course covers elementary discrete mathematics. Use ocw to guide your own lifelong learning, or to teach others. The readings for each week are from the course textbook, discrete mathematics and its applications, fourth edition, by kenneth h. Support for mit opencoursewares 15th anniversary is provided by. Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart.
Cohen micohen at mit dot edu, christopher musco, ali vakilian. Sep 12, 2016 mix play all mix mit opencourseware youtube 111 videos play all mit 6. Discrete geometry lectures on discrete geometry matousek. Mit opencourseware makes the materials used in the teaching of almost all of mits subjects available on the web, free of charge. Textbooks math and statistics this is a revised mathematics subject guide. What is the best book for studying discrete mathematics. This course will roughly cover the following topics and speci c applications in computer science. With more than 2,200 courses available, ocw is delivering on the promise of open sharing of knowledge. Topics include probability, counting, linear programming, numbertheoretic algorithms, sorting, data compression, and errorcorrecting codes.
Mathematics with computer science course 18c book is pretty common for that. A lot of students hate foundations as it appears that it has no practical purpose when you take it. The special event for fall 2008 is that the lectures will be recorded for opencourseware you will already find a partial earlier set on the website but the course has since evolved. I am using resources from nptel, mit ocw, and arsdigita university. Mathematics for computer science mit opencourseware. It is increasingly being applied in the practical fields of mathematics and computer science. Ocw is a free and open publication of material from thousands of mit courses, covering the entire mit curriculum. The mission of the department of mathematics is to support the mission of the university by providing mathematics majors with high quality programs. It is a very good tool for improving reasoning and problemsolving capabilities. Binary stars, neutron stars, black holes, resonance phenomena, musical instruments, stellar. Mit opencourseware ocw is a free, publicly accessible, openlylicensed digital collection of highquality teaching and learning materials, presented in an easily accessible format. Got an a in discrete 1 proof methods using epps book at community college with an easier professor the only offering for that course, and im understanding nothing to very little amount of information in discrete 2 computational, graph theory, etc. We will follow the 2008 outline or indeed the video lectures fairly closely perhaps with a slight more emphasis on computing. Mix play all mix mit opencourseware youtube 111 videos play all mit 6.
The literature used is discrete mathematics and its applications by kenneth h. There are 4 different versions, 2010 spring, 2010 fall, 2005 spring and 2005 fall. Mathematics mit opencourseware free online course materials. Mit opencourseware makes the materials used in the teaching of almost all of mit s subjects available on the web, free of charge. Pair the book with an mit ocw math for computer science or something similar and you should be more than good.
Discrete mathematics and its applications by knneth rosen. Discrete mathematics is in contrast to continuous mathematics, which deals with structures which can range in value over the real numbers, or. You will need to have done very well in these courses to keep up with the pace. Tomorrow wednesdays exam will cover fourier series, a discrete convolution computation, circulant matrices, and a fourier integral. Discrete mathematics function topic physics forums. I am currently going through susanna epps discrete mathematics with applications. Discrete maths is a study of things which are discrete, which means things which can be counted. Differential equations mathematics mit opencourseware. If you dont know how to program this book will teach you by modeling math functions in sml, polynomials into lists, sets into types, creating relations and proving their results with programs. I have encountered most of the topics from that book. Finding the best discrete math examples vgs golfer. Discrete mathematics forms the mathematical foundation of computer and information science.
The laws of nature are expressed as differential equations. This calendar shows the weekly schedule for the course, which usually includes three lecture and group problem solving sessions per week. The lists below show a few titles for some broad and specific subjects. Mit faculty and instructional staff, and its codomain is the set, subnums, of subject. Mathematics course 18 discrete mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. Topics include probability, counting, linear programming, numbertheoretic algorithms, sorting. What are the best online resources to learn discrete. This is indeed an uptotheminute text pdf, dated mar 7, 2017. Mathematical definitions and proofs are emphasized. I am using youtube, other books including rosens excellent discrete mathematics and its. Discrete mathematics for computer scientists 1, stein. Bachelor of science in mathematics with computer science general institute requirements girs the general institute requirements include a communication requirement that is integrated into both the hass requirement and the requirements of each major. Ive heard that the course provided by mit ocw is quite excellent. The two programs in pure and applied mathematics offer basic and advanced classes in analysis, algebra, geometry, lie theory, logic, number theory, probability, statistics, topology, astrophysics, combinatorics, fluid dynamics, numerical analysis, theoretical physics, and the theory of computation.
Just start reading the book any discrete mathematics book. Jan 24, 2017 got an a in discrete 1 proof methods using epps book at community college with an easier professor the only offering for that course, and im understanding nothing to very little amount of information in discrete 2 computational, graph theory, etc. Jun 24, 2019 math is extremely vital and is is a large and important aspect of life in so many different ways. Licensed under the creative commons attribution noncommercial license unless otherwise noted. It is already has problem sets, exercises and lectures notes. Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Examples of structures that are discrete are combinations, graphs, and logical statements. I tried math for computer science on mit ocw but it was lacking solutions, which made it really hard for selflearning. To be honest, it best depends on your learning style which course may be best for you or not. Mar 06, 2017 this fall i will be teaching the required discrete math for cs course to about fifty students at the university of south carolina.
Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable. With more than 2,400 courses available, ocw is delivering on the promise of open sharing of knowledge. Others are selfpublished online books, or course notes which are so thorough that they serve as an. This is an introductory course in discrete mathematics oriented toward computer science and engineering. Definitions, proofs, sets, functions, relations discrete structures. This is a basic course on matrix theory and linear algebra. Mathematics course 18 book covers most of the topics in courses 15251 and 15150, and teaches you to write proofs as programs. Lots and a lot of entire books are written about graphs.
This is a communication intensive in the major cim course, and thus includes a writing component. Discrete maths forms the basis of a lot of concepts in algorithms and computer science in general. There are some courses on mit ocw, which includes videos, problem sets, and quizzes. What i have encountered also is the definitions of functions in terms of images and mappings.
In addition to the basic concepts of newtonian mechanics, fluid mechanics, and kinetic gas theory, a variety of interesting topics are covered in this course. For 2010 exams will be in class, open book and open notes, not evenings, no computers. Well target specifically the third sort of model, since it is what we would like to assess. In pure mathematics we explore exciting current research directions in most of the major fields. Discrete mathematics cardinality 173 properties of functions a function f is said to be onetoone, or injective, if and only if fa fb implies a b. Faculty alumni visitors giving persons with disabilities. It emphasizes mathematical definitions and proofs as well as. I dont own it, but i would suspect that it either provides the answers to the other half of the questions or provides a stepbystep guide to. Discrete mathematics and its applications kenneth rosen. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
The best complete online resources for discrete mathematics is mit ocw mathematics for computer science. Perhaps more importantly, they will reach a certain. The science hayden, barker, and dewey libraries hold several mathematics and applied mathematics textbooks. I am currently taking a course in discrete mathematics.
A very good textbook for discrete mathematics at an undergraduate level is the kenneth rosen book titled discrete mathematics and its applications the book provides solutions to half of the problems. This book covers most of the topics in courses 15251 and 15150, and teaches you to write proofs as programs. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. Online textbooks mit opencourseware free online course. I am using youtube, other books including rosens excellent discrete mathematics and its applications, concrete mathematics, the mit ocw course in mathematics for computer science, and a variety of other materials to try and make it through this course. A gentle introduction to discrete math featuring python by allan m. Undergraduate seminar in discrete mathematics spring 2015 undergraduate 18. Principles of discrete applied mathematics mathematics. These notes are courtesy of eric lehman, tom leighton, and albert meyer, and are used with permission.
Principles of discrete applied mathematics mit opencourseware. This course is an introduction to discrete applied mathematics. This course covers elementary discrete mathematics for computer science and engineering. Not sure if the problem sets are the same as the one in the text. Solutions to mathematics for computer science problems. What are the best online resources to learn discrete mathematics. Number theory athe math behind the rsa crypto system. A lot of the answers allude to different university discrete math classes, which makes it a really good start. Complex functions from calculating the trajectory of a satellite past a planet, to more practical tasks such as working out how much you owe the cashier at the supermarket.
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