Free download скачать Discrete Mathematics With Computer Science Applications
Published 8/2025
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 1.58 GB | Duration: 7h 0m
Learn discrete math and translate it to applications like computer algorithms and arithmetic, and digital logic circuits

What you'll learn
Number bases and binary arithmetic, including how numbers are stored in computer memory
Mathematical algorithms and their applications, including computer graphics, games and cryptography
Understand iteration and recursion using sequences and series
Solving recurrence relations
Analysing the computational complexity of searching and sorting algorithms using the Big-O notation
Understand combinatorics and enumeration
Boolean algebra, truth tables and switching circuits
Using Karnaugh maps to build digital logic circuits
Requirements
Basic algebra and arithmetic
Description
This course is designed to make learning Discrete Mathematics easy. It is well-arranged into targeted sections of focused lectures and extensive worked examples to give you a solid foundation in the key topics from theory to applications.The course is ideal for:Discrete math students who want to be at the top of their class or get ahead of their classAny person who is interested in mathematics and/or needs a refresher courseAny person who is undertaking a discipline that requires discrete math, including graphics, games programming, analysis of algorithms, digital electronics and logic circuits, cryptography, and so onAt the end of this course, you will have a strong foundation in one of the most important disciplines of Mathematics, which you will definitely come across if you are from a computer science or engineering background. I welcome any questions and provide a friendly Q&A forum where I aim to respond to you in a timely manner. Enrol today and you will get:Lifetime access to refer back to the course whenever you need toFriendly Q&A forumUdemy Certificate of Completion30-day money back guaranteeThe course covers the following core units and topics of Discrete Mathematics:1) Number bases and binary arithmetica) Introduction to number bases (decimal, binary, hexadecimal and octal)b) Converting between decimal, binary, hexadecimal and octalc) Adding, subtracting, multiplying and dividing binary and hexadecimal numbersd) Subtracting using complements (ten's and two's complement)e) Normalised scientific notationf) Representing real numbers in computer memory using the IEEE754 floating point standard2) Mathematical Computer Algorithmsa) Intro to computer algorithms and writing pseudocodeb) Horner's algorithm for evaluating polynomialsc) Collision detection algorithm in computer graphics and gamesd) Encryption and decryption algorithm in cryptographye) Lottery combination algorithm3) Iteration and Recursiona) Review of sigma (or summation) notationb) Deriving the geometric and arithmetic seriesc) Computing the Fibonacci sequence iteratively and recursivelyd) Factorial sequence recurrence relation4) Recurrence Relationsa) Intro to recurrence relations, standard form and propertiesb) General solution to homogeneous first and second order recurrence relationsc) Method of solution for non-homogeneous second order recurrence relationsd) Special cases of the general solution to non-homogeneous second order recurrence relations5) Computational Complexity of Algorithms and Big O Notationa) Intro to computational complexityb) Informal definition of Big Oc) Comparing growth rates, logarithmsd) Typical growth rates (constant, log, linear, quadratic and so on)e) Formal definition of Big Of) Refining Big O calculations using the triangle inequality and obtaining better constantsg) Big O analysis of search and sort algorithms6) Combinatorics and Enumerationa) Multiplication and addition rules of countingb) Inclusion-exclusion principlec) Permutations and the r-permutationd) Permutations vs combinationse) Combinations and multiple categoriesf) Binomial theoremg) Lexicographic orderingh) Cartesian product of sets7) Boolean Algebraa) Review of functionsb) Binary operationsc) Boolean algebra, truth tables and axiomsd) Switching circuitse) de Morgan's laws, dual interchangef) Equivalence of boolean expressionsg) Minterm and disjunctive normal form8) Karnaugh Maps and Digital Logic Circuitsa) Karnaugh mapsb) Karnaugh map algorithm for obtaining the minimal boolean expressionc) Don't care Karnaugh mapsd) Logic and logic circuitse) How a breadboard worksf) Building a logic circuit with a NOT, AND and XOR gateg) Building half-adder and full-adder logic circuitsh) Building two-bit and four-bit adder logic circuitsi) Building a two's complement logic circuit for representing negative binary numbersj) Building a logic circuit for subtracting binary numbers
Mathematics or computer science students looking to get ahead of their class,Any person who is interested in mathematics and/or needs a refresher course,Any person who is undertaking a discipline that requires discrete math, including graphics, games programming, analysis of algorithms, digital electronics and logic circuits, cryptography, and so on
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