課程介紹

This course covers all Mathematics needed to become Software Developer. Here we will discuss Linear Algebra, Modern Analysis, Mathematical Logic, Number Theory and Discrete Mathematics. By the end of this course you will be able to analyze and descri

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哪些人適合這堂課？

• Beginner Java Developers
• Beginner Python Developers
• Beginner C & C++ Developers
• Computer Science Students
• Engineering Students
• Employees in Programming Companies

學習目標

• Proof Techniques. Mathematical Induction and Recursion Theory.
• Mathematical Logic. Propositional and First Order Calculus. Model Theorem.
• Programs verifications and Model Checking
• Linear Algebra. Matrix Theory in Computer Science.
• Boolean Algebra and its applications in Digital Electronics.
• Lambda Calculus as a Foundation of Functional Programming
• Number Theory and Encryption.
• Modern Statistics and Probabilistic Methods in Computer Science.
• Functional Analysis and the efficiency of computer algorithms Decision Theory

課程介紹

MASTER DISCRETE MATH 2020 IS SET UP TO MAKE DISCRETE MATH EASY:

This 461-lesson course includes video and text explanations of everything from Discrete Math, and it includes 150 quizzes (with solutions!) after each lecture to check your understandin

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哪些人適合這堂課？

• This course is for anyone who wants to learn about Discrete Mathematics, regardless of previous experience
• It’s perfect for complete beginners with zero experience in Discrete Mathematics
• It’s also perfect for students who have a decent understanding of Discrete Mathematics but wish to learn even more advanced material
• If you want to take ONE COURSE to learn everything you need to know about Discrete Mathematics, take this course

學習目標

• Analyze and interpret the truth value of statements by identifying logical connectives, quantification and the truth value of each atomic component
• Distinguish between various set theory notations and apply set theory concepts to construct new sets from old ones
• Interpret functions from the perspective of set theory and differentiate between injective, surjective and bijective functions
• Construct new relations, including equivalence relations and partial orderings
• Apply the additive and multiplicative principles to count disorganized sets effectively and efficiently
• Synthesize counting techniques developed from counting bit strings, lattice paths and binomial coefficients
• Formulate counting techniques to approach complex counting problems using both permutations and combinations
• Prove certain formulas are true using special combinatorial proofs and complex counting techniques involving stars and bars
• Connect between complex counting problems and counting functions with certain properties
• Develop recurrence relations and closed formulas for various sequences
• Explain various relationships and properties involving arithmetic and geometric sequences
• Solve many recurrence relations using polynomial fitting
• Utilize the characteristic polynomial to solve challenging recurrence relations
• Master mathematical induction and strong induction to prove sophisticated statements involving natural numbers by working through dozens of examples
• Use truth tables and Boolean Algebra to determine the truth value of complex molecular statements
• Apply various proving techniques, including direct proofs, proof by contrapositive and proof by contradiction to prove various mathematical statements
• Analyze various graphs using new definitions from graph theory
• Discover many various properties and algorithms involving trees in graph theory
• Determine various properties of planar graphs using Euler’s Formula
• Categorize different types of graphs based on various coloring schemes
• Create various properties of Euler paths and circuits and Hamiltonian paths and cycles
• Apply concepts from graph theory, including properties of bipartite graphs and matching problems
• Use generating functions to easily solve extremely sophisticated recurrence relations
• Develop a deep understanding of number theory which involve patterns in the natural numbers

課程介紹

WHAT IS THIS COURSE ABOUT?

Discrete Mathematics (DM), or Discrete Math is the backbone of Mathematics and Computer Science. DM is the study of topics that are discrete rather than continuous, for that, the course is a MUST for any Math or CS student

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哪些人適合這堂課？

• This course is designed for students majoring or minoring in Computer Science, Mathematics, Mathematics Education, and Engineering.

學習目標

• You will learn and develop the ability to think, read and write abstractly and Mathematically.
• You will learn the fundamentals of Set Theory including set builder notation, and set operations and properties.
• You will learn tautologies, contradictions, De Morgan’s Laws in Logic, logical equivalence, and formulating quantified statements.
• You will lear how to create truth tables and tell the falsehood and truthfulness of a compound statements.
• You will know how to write, read and prove Mathematical statements using a variety of methods.
• You will understand boolean expressions, black boxes, logical gates and digital circuits.
• You will understand the Fundamental Theorem of Arithmetics, modular arithmetic, and learn how to find GCD & LCM.
• You will acquire a solid foundation in functions, function composition & combination, bijective and inverse functions.
• You will learn how to find equivalence relations and equivalence classes.
• You will learn essential concepts in Statistics and Combinatorics.
• You will master arithmetic and geometric sequences, and partial sums.
• You will learn the fundamental concepts in Graph Theory like incidence and adjacency matrices, walks, eccentricity, hamiltonian paths and circuits, connectedness, and Ore’s Theorem.

課程介紹

All new quiz solution videos plus an additional graph theory section to help students master all aspects of Discrete Math!

Welcome to Master Discrete Math! 

This is a course designed to help you master the difficult topics of Discrete Math and get

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哪些人適合這堂課？

• Computer Science Majors
• Math Majors
• People interested in the math behind computers
• People interested in mathematical logic
• Anyone wanting to expand their mathematical knowledge

學習目標

• Most Complete Course on Discrete Math offered on Udemy
• Fully Understand Mathematical Logic
• Grasp the Complex Topic of Counting for Advanced Mathematics
• Know When to Use Combinations or Permutations
• Solve Real World Problems Using Combinations and Permutations
• Discover How to Solve Mathematical Proofs Using a Variety of Methods
• Learn Mathematical Notation to be able to Understand Complex Proofs

課程介紹

What is this course about?

Graph Theory is an advanced topic in Mathematics. On a university level, this topic is taken by senior students majoring in Mathematics or Computer Science; however, this course will offer you the opportunity to obtain a s

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哪些人適合這堂課？

• Mathematics or Computer Science students
• Anyone interested in learning advanced Mathematics in an easy way

學習目標

• Master fundamental concepts in Graph Theory
• Understand Eulerian and Hamiltonian paths and circuits. And many related topics to Paths.
• Get to know a wide range of different Graphs, and their properties.
• Be able to preform Elementary, Advanced Operations on Graphs to produce a new Graph
• Understand Graph Coloring.
• Know how to turn a Graph into a Matrix and vice versa.
• Obtain a solid foundation in Trees, Tree Traversals, and Expression Trees.

課程介紹

Welcome to this course on Discrete Math. In this course you will learn Set Theory, Relations, Functions and Mathematical Induction.

Discrete Math is the real world mathematics. It is the mathematics of computing. The mathematics of modern computer s

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哪些人適合這堂課？

• Math Students.
• Computer Programmers/Computer Science Students.
• Engineering Majors.
• Working Professionals.
• Anybody who learnt Discrete Math long time and want to refresh his/her knowledge.

學習目標

• Discrete Math-Set Theory, Relations, Functions and Mathematical Induction!
• More than 1,700 students from 120 countries!
• Over 6.5 hours of Learning!
• Lifetime Access!
• Certificate of Completion for your Job Interviews!
• By the end of this course, you will be able to define a set and represent the same in different forms;
• define different types of sets such as, finite and infinite sets, empty set, singleton set, equivalent sets, equal sets, sub sets, proper subsets, supersets, give examples of each kind of set, and solve problems based on them;
• define union and intersection of two sets, and solve problems based on them;
• define universal set, complement of a set, difference between two sets, and solve problems based on them;
• define Cartesian product of two sets, and solve problems based on them;
• represent union and intersection of two sets, universal sets, complement of a set, difference between two sets by Venn Diagram;
• solve problems based on Venn Diagram;
• define relation and quote examples of relations;
• find the domain and range of a relation;
• represent relations diagrammatically;
• define different types of relations such as, empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, equivalence relation, and solve problems based on them;
• define function and give examples of functions;
• find the domain, codomain and range of a function;
• define the different types of functions such as injective function (one-to-one function), surjective function (onto function), bijective function, give examples of each kind of function, and solve problems based on them.
• define and give examples of even and odd functions;
• figure out if any given function is even, odd, or neither from graphs as well as equations;
• define composition of two functions;
• find the composition of functions;
• define the inverse of a function;
• find the inverse of any given function;
• find the domain and range of the inverse function;
• Understand the concept of Mathematical Induction and the logic behind it;
• Learn to prove statements using Mathematical Induction;
• Learn to apply Mathematical Induction in a Brain Teasing Real World Problem;
• Understand the application of Mathematical Induction in Computer Program/Algorithm Correctness Proofs;
• Learn to apply Mathematical Induction for proving a Result from Geometry;
• Learn to apply Mathematical Induction for proving the Divisibilities;
• Learn to apply Mathematical Induction for proving the sum of Arithmetic Progressions;
• Learn to apply Mathematical Induction for proving the the Sum of squares of first n natural numbers;
• Learn to apply Mathematical Induction for proving the Inequalities;
• Learn to apply Mathematical Induction for proving the sum of Geometric Progressions.

課程介紹

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The prerequisite to the course Discrete Mathematics: Open Doors to Great Careers 2.

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哪些人適合這堂課？

• Working Professionals
• Anyone interested in gaining mastery of the core topics in Discrete Mathematics
• Adult Learners
• College Students

學習目標

• Refresh your math knowledge.
• Gain a firm foundation in Discrete Mathematics for furthering your career.
• Learn one of the mathematical subjects crucial for Computer Science.
• Learn one of the mathematical subjects needed for Data Science.

課程介紹

世界上所有電腦科學、資訊工程、資料管理主修的學生，都在學習電腦科學!

隨著電腦科學的飛速發展，離散數學的重要性則日益彰顯。它為許多資訊學課程提供了數學基礎，包括資料結構、演算法、資料庫理論、形式語言與作業系統等。如果沒有離散數學的相關數學基礎，學生在學習上述課程中，便會遇到較多的困難。

離散數學包含邏輯、證明、遞迴關係、演算法、數論與密碼學、演算法分析、圖形理論、路徑選擇、機率、排列組合、以及其他重要的程式開發演算法! 這堂課會深入淺出探討這些概念，並且用 Python 或JavaScrip

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哪些人適合這堂課？

• 對資料科學、機器學習、人工智慧有興趣的Python開發工程師
• 對網頁前端後端有興趣，能夠使用基本JavaScript的工程師
• 正在大學就讀資訊工程、電腦科學、資料科學、數學的學生
• 對於電腦科學、資訊管理、資訊工程有興趣的任何人
• 對於研究應用數學有興趣的人
• 正在準備學習演算法以及資料結構的人

學習目標

• 數學邏輯運算與程式邏輯推演
• 以遞迴演算法實現數學歸納法邏輯與證明
• 使用遞迴演算法，計算遞迴函數與「線性遞迴關係式」，並用程式碼計算「斐波那契數列」
• 學習集合理論與機率
• 用程式碼計算排列組合以及電腦計算複雜度
• 學習電腦科學中的圖形理論以及演算法，判斷圖形資料結構
• 學會「歐幾里得演算法」，包括數學應用與程式碼，並應用於計算數論問題
• 使用「歐拉函數」與在密碼學中使用
• 用遞迴函數計算「河內塔問題」，以及找出並歸納河內塔問題公式
• 使用Floyd-Warshall 演算法 (Dynamic Programming)解決路徑問題
• 了解圖形演算法中的「Dijkstra’s Algorithm」、「Depth First Traversal」、「Breadth First Traversal」。
• 用 Python 或 JavaScript 來實現離散數學的演算法與架構!

課程介紹

Are you struggling with the basic mathematical skill you need as a computer scientist?

Are you unhappy with your instructor’s ability to teach the fundamental skills you need to do well in your math courses?

Master Discrete Mathematics: Set Theory

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哪些人適合這堂課？

• This course is meant for undergraduate computer scientists, math majors, or anyone with an interest in the fundamentals of mathematics.

學習目標

• Ace your set theory exam questions
• Given two or more sets, find subsets, power sets, intersections, unions, differences, and complements of those sets.
• Given two sets, determine, using set laws and venn diagrams, if the two sets are equal.

課程介紹

You’ve just stumbled upon the most in-depth Discrete Math course series online. With over 15,000 students enrolled and thousands of 5 star reviews to date in the area of computer science, my computer science courses are enjoyed by students from 130 c

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哪些人適合這堂課？

• Any computer science student
• Anybody who is interested to do a research in computer science
• Any Engineer who wants to build logical thinking
• Anybody who likes to analyse mathematics
• Any body who is preparing for exams like GATE , PGEE , ISRO etc.
• Anybody who wants to master propositional logic
• Anybody who wants to understand advanced concepts of Discrete Mathematics
• Anybody who wants to learn Discrete Mathematics from scratch
• Anyone who wants to learn set theory from scratch

學習目標

• Master Discrete Mathematics
• Master propositional logic
• Get ready for advanced topics of computer science
• Get ready for research in computer science