Master Discrete Math 2020 More Than 5 Complete Courses In 1

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Last updated 6/2020
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 9.85 GB | Duration: 16h 3m
Learn Discrete Mathematics In This Course: 300+ Lectures/Quizzes And 30 Assignments With 500+ Questions & Solutions

What you'll learn
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
Requirements
You should be comfortable with high school algebra
Be ready to learn an insane amount of awesome stuff
Prepare to succeed in any college level Discrete Math course
Brace yourself for tons of content
Description
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 understanding and an additional 30 workbooks with 500+ extra practice problems (also with solutions to every problem!), to help you test your understanding along the way.This is the most comprehensive, yet straight-forward, course for Discrete Mathematics on Udemy! Whether you have never been great at mathematics, or you want to learn about the advanced features of Discrete Math, this course is for you! In this course we will teach you Discrete Mathematics.Master Discrete Math 2020 is organized into the following 24 sections:Mathematical StatementsSet TheoryFunctions And Function NotationRelationsAdditive And Multiplicative PrinciplesBinomial CoefficientsCombinations And PermutationsCombinatorial ProofsAdvanced Counting Using The Principle Of Inclusion And ExclusionDescribing SequencesArithmetic And Geometric SequencesPolynomial FittingSolving Recurrence RelationsMathematical InductionPropositional LogicProofs And Proving TechniquesGraph Theory DefinitionsTreesPlanar GraphsColoring GraphsEuler Paths And CircuitsMatching In Bipartite GraphsGenerating FunctionsNumber TheoryAND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:Videos: Watch engaging content involving interactive whiteboard lectures as I solve problems for every single math issue you'll encounter in discrete math. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.Notes: The notes section of each lesson is where you find the most important things to remember. It's like Cliff Notes for books, but for Discrete Math. Everything you need to know to pass your class and nothing you don't.Quizzes: When you think you've got a good grasp on a topic within a lecture, test your understanding with a quiz. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbooks. These workbooks include 500+ extra practice problems (all with detailed solutions and explanations for how to get to those solutions), so they're a great way to solidify what you just learned in that section.YOU'LL ALSO GET:Lifetime access to a free online Discrete Math textbookLifetime access to Master Discrete Math 2020Friendly support in the Q&A sectionUdemy Certificate of Completion available for downloadSo what are you waiting for? Learn Discrete Math in a way that will advance your career and increase your knowledge, all in a fun and practical way!HERE'S WHAT SOME STUDENTS OF MASTER DISCRETE MATH 2020 HAVE TOLD ME:"The course covers a lot of Discrete Math topics helping someone like me who knew nothing about discrete mathematics. The course structure is well-arranged and the explanation for every topic is given in a very simple manner. It helped me a lot. I really want to thank the instructor for helping me to explore this amazing world of Discrete Math." - Shibbu J."This course is great. Discrete Math is difficult, but Amour's explanations are very clear. I have bought other math courses by Kody Amour and all of them are great, well-explained and easy to follow." - Susan M."Very comprehensive course and exceptionally articulated." - Faisal Abbas"Best course for Discrete Maths on Udemy." - Vatsal P.Will this course give you core discrete math skills?Yes it will. There are a range of exciting opportunities for students who take Discrete Math. All of them require a solid understanding of Discrete Math, and that's what you will learn in this course.Why should you take this course?Discrete Mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. Discrete means individual, separate, distinguishable implying discontinuous or not continuous, so integers are discrete in this sense even though they are countable in the sense that you can use them to count. The term "Discrete Mathematics" is therefore used in contrast with "Continuous Mathematics," which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.Almost all middle or junior high schools and high schools across the country closely follow a standard mathematics curriculum with a focus on "Continuous Mathematics." The typical sequence includes:Pre-Algebra -> Algebra 1 -> Geometry -> Algebra 2/Trigonometry -> Precalculus -> Calculus Multivariable Calculus/Differential EquationsDiscrete mathematics has not yet been considered a separate strand in middle and high school mathematics curricula. Discrete mathematics has never been included in middle and high school high-stakes standardized tests in the USA. The two major standardized college entrance tests: the SAT and ACT, do not cover discrete mathematics topics.Discrete mathematics grew out of the mathematical sciences' response to the need for a better understanding of the combinatorial bases of the mathematics used in the real world. It has become increasingly emphasized in the current educational climate due to following reasons:Many problems in middle and high school math competitions focus on discrete mathApproximately 30-40% of questions in premier national middle and high school mathematics competitions, such as the AMC (American Mathematics Competitions), focus on discrete mathematics. More than half of the problems in the high level math contests, such as the AIME (American Invitational Mathematics Examination), are associated with discrete mathematics. Students not having enough knowledge and skills in discrete mathematics can't do well on these competitions. Our AMC prep course curriculum always includes at least one-third of the studies in discrete mathematics, such as number theory, combinatorics, and graph theory, due to the significance of these topics in the AMC contestsDiscrete Mathematics is the backbone of Computer ScienceDiscrete mathematics has become popular in recent decades because of its applications to computer science. Discrete mathematics is the mathematical language of computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are tremendously significant in applying ideas from discrete mathematics to real-world applications, such as in operations research.The set of objects studied in discrete mathematics can be finite or infinite. In real-world applications, the set of objects of interest are mainly finite, the study of which is often called finite mathematics. In some mathematics curricula, the term "finite mathematics" refers to courses that cover discrete mathematical concepts for business, while "discrete mathematics" courses emphasize discrete mathematical concepts for computer science majors.Discrete math plays the significant role in big data analytics.The Big Data era poses a critically difficult challenge and striking development opportunities: how to efficiently turn massively large data into valuable information and meaningful knowledge. Discrete mathematics produces a significant collection of powerful methods, including mathematical tools for understanding and managing very high-dimensional data, inference systems for drawing sound conclusions from large and noisy data sets, and algorithms for scaling computations up to very large sizes. Discrete mathematics is the mathematical language of data science, and as such, its importance has increased dramatically in recent decades.IN SUMMARY, discrete mathematics is an exciting and appropriate vehicle for working toward and achieving the goal of educating informed citizens who are better able to function in our increasingly technological society; have better reasoning power and problem-solving skills; are aware of the importance of mathematics in our society; and are prepared for future careers which will require new and more sophisticated analytical and technical tools. It is an excellent tool for improving reasoning and problem-solving abilities.Starting from the 6th grade, students should some effort into studying fundamental discrete math, especially combinatorics, graph theory, discrete geometry, number theory, and discrete probability. Students, even possessing very little knowledge and skills in elementary arithmetic and algebra, can join our competitive mathematics classes to begin learning and studying discrete mathematics.Does the course get updated?It's no secret how discrete math curriculum is advancing at a rapid rate. New, more complex content and topics are changing Discrete Math courses across the world every day, meaning it's crucial to stay on top with the latest knowledge.A lot of other courses on Udemy get released once, and never get updated. Learning from an outdated course and/or an outdated version of Discrete Math can be counter productive and even worse - it could teach you the wrong way to do things.There's no risk either!This course comes with a full 30 day money-back guarantee. Meaning if you are not completely satisfied with the course or your progress, simply let Kody know and he will refund you 100%, every last penny no questions asked.You either end up with Discrete Math skills, go on to succeed in college level discrete math courses and potentially make an awesome career for yourself, or you try the course and simply get all your money back if you don't like it.You literally can't lose. Ready to get started?Enroll now using the "Add to Cart" button on the right, and get started on your way to becoming a master of Discrete Mathematics. Or, take this course for a free spin using the preview feature, so you know you're 100% certain this course is for you.See you on the inside (hurry, your Discrete Math class is waiting!)Some content was used from Creative Commons, and attribution is provided within the curriculum of this course.
Overview
Section 1: Introduction
Lecture 1 Welcome To Discrete Mathematics!
Lecture 2 What Is Discrete Mathematics?
Lecture 3 Why Study Discrete Mathematics?
Lecture 4 Who Should You Take Discrete Mathematics?
Lecture 5 How To Obtain Your Free Textbook
Section 2: PART 1.1 (FOUNDATIONS): MATHEMATICAL STATEMENTS - Analyze Truth In Statements
Lecture 6 Mathematical Statements In Discrete Math
Lecture 7 Atomic And Molecular Statements - How To Break Apart Complex Statements
Lecture 8 An Overview Of Implications
Lecture 9 Direct Proofs Of Implications
Lecture 10 What Is The Converse And The Contrapositive Of A Statement?
Lecture 11 The Dreaded If And Only If Connective
Lecture 12 What Does It Mean To Be Necessary And Sufficient?
Lecture 13 What Exactly Are Free Variables and Predicates?
Lecture 14 What Are Universal Quantifiers And Existential Quantifiers?
Lecture 15 How To Properly Negate Quantifiers
Lecture 16 How To Unravel Implicit Quantifiers (Or Hidden Quantifiers)
Section 3: PART 1.2 (FOUNDATIONS): SET THEORY - Construct New Sets From Old Sets
Lecture 17 Introduction To Sets In Discrete Math
Lecture 18 An Overview Of Set Notation
Lecture 19 What Is Set Builder Notation?
Lecture 20 A Complete Review Of Set Theory Notation
Lecture 21 Interpreting Relationships Between Sets
Lecture 22 What Is The Power Set?
Lecture 23 Cardinality - How To Count Elements Of Sets
Lecture 24 Operations On Sets - Making New Sets From Old Sets
Lecture 25 How To Combine Sets With The Cartesian Product
Lecture 26 Venn Diagrams - A Complete Introduction
Section 4: PART 1.3 (FOUNDATIONS): FUNCTIONS AND FUNCTION NOTATION - Apply Set Theory
Lecture 27 What Are Functions In Discrete Math?
Lecture 28 How To Interpret Functions With Set Theory - Part One
Lecture 29 How To Interpret Functions With Set Theory - Part Two
Lecture 30 What Are Recursively Defined Functions?
Lecture 31 Introduction To Surjective, Injective And Bijective Functions
Lecture 32 The Difference Between Injective And Surjective Functions
Lecture 33 Image And Inverse Image - A Closer Look Into The Codomain
Lecture 34 A Complete List Of Function Definitions
Section 5: PART 1.4 (FOUNDATIONS): RELATIONS - Construct Relationships Within Sets
Lecture 35 What Is A Relation Between Sets?
Lecture 36 Equivalence Relations - Reflexive, Symmetric And Transitive
Lecture 37 Partially Ordered Sets (Posets) - Asymmetry And Totally Ordered Sets
Section 6: PART 2.1: ADDITIVE AND MULTIPLICATIVE PRINCIPLES - Count Disorganized Sets Well
Lecture 38 What Is The Additive Principle?
Lecture 39 What Is The Multiplicative Principle?
Lecture 40 How To Count Sets In Discrete Math
Lecture 41 Revisiting The Additive Principle With Sets
Lecture 42 Using The Cartesian Product To Interpret The Multiplicative Principle With Sets
Lecture 43 What Is The Principle Of Inclusion And Exclusion - Cardinality Of A Set Union
Lecture 44 Computing The Cardinality Of A Union Between Three Sets
Section 7: PART 2.2: BINOMIAL COEFFICIENTS - Count Bit Strings, Lattice Paths And Much More
Lecture 45 Subsets - Revisiting Set Theory
Lecture 46 What Are Bit Strings?
Lecture 47 What Are Lattice Paths?
Lecture 48 An Introduction To Binomial Coefficients
Lecture 49 A Complete List Of Interpretations Of Binomial Coefficients
Lecture 50 What Is The Recurrence Relation For The Binomial Coefficient?
Lecture 51 A Deep Explanation Of Pascal's Triangle
Section 8: PART 2.3: COMBINATIONS AND PERMUTATIONS - Formulate Complex Counting Techniques
Lecture 52 An Introduction To Permutations In Discrete Math
Lecture 53 A Closer Look Into k-Permutations Of n Elements
Lecture 54 The Closed Formula For The Binomial Coefficient
Section 9: PART 2.4: COMBINATORIAL PROOFS - Apply Special Combinations
Lecture 55 What Are The Patterns In Pascal's Triangle & Binomial Identities
Lecture 56 An Introduction To Combinatorial Proofs
Lecture 57 Introduction To Stars And Bars - Part One
Lecture 58 Introduction To Stars And Bars - Part Two
Section 10: PART 2.5: ADVANCED PRINCIPLE OF INCLUSION AND EXCLUSION - Avoid Double Counting
Lecture 59 Advanced Counting Using The Principle Of Inclusion And Exclusion
Lecture 60 How Do You Count Derangements?
Lecture 61 An Introduction To Counting Functions With Unique Properties
Lecture 62 How To Count Surjective Functions Using The Principle Of Inclusion Exclusion
Lecture 63 How To Count Functions To Solve Problems From Different Contexts
Section 11: PART 2.6: COUNTING REVIEW WITH DETAILED SOLUTIONS
Section 12: PART 3.1: DESCRIBING SEQUENCES - Recurrence Relations And Closed Formulas
Lecture 64 How To Interpret Sequences
Lecture 65 Closed Formulas For Sequences Versus Recursive Definitions
Lecture 66 Examples Of Sequences With Closed Formulas And Recursive Definitions
Lecture 67 How To Construct Sequences Using Partial Sums
Section 13: PART 3.2: ARITHMETIC AND GEOMETRIC SEQUENCES - Explain Various Relationships
Lecture 68 Introduction To Arithmetic Sequences
Lecture 69 Introduction To Geometric Sequences
Lecture 70 Computing Sums Of Arithmetic And Geometric Sequences
Lecture 71 Summing Arithmetic Sequences: Reverse And Add
Lecture 72 Summing Geometric Sequences: Multiply, Shift And Subtract
Section 14: PART 3.3: POLYNOMIAL FITTING - Solve Many Recurrence Relations With Polynomials
Lecture 73 What Is Polynomial Fitting?
Lecture 74 What Are Finite Differences?
Section 15: PART 3.4: SOLVING RECURRENCE RELATIONS - Apply Characteristic Polynomials
Lecture 75 How To Solve Recurrence Relations
Lecture 76 What Are Telescoping Sequences?
Lecture 77 Utilizing Iterations To Interpret Recurrence Relations
Lecture 78 An Overview Of The Characteristic Root Technique
Lecture 79 What Is The Characteristic Polynomial And The Characteristic Equation?
Lecture 80 How To Use The Characteristic Root Technique For Repeated Roots
Section 16: PART 3.5: MATHEMATICAL INDUCTION - Prove Statements With Natural Numbers
Lecture 81 An Introduction To Induction - An Advanced Proving Technique
Lecture 82 How To Interpret The Base Case And The Inductive Case In Induction
Lecture 83 How To Formalize Proofs In Discrete Math
Lecture 84 An Overview Of The Induction Proof Structure
Lecture 85 Our First Example Of Using Mathematical Induction
Lecture 86 Our Second Example Of Using Mathematical Induction
Lecture 87 Our Third Example Of Using Mathematical Induction
Lecture 88 A Warning About Mathematical Induction
Lecture 89 Strong Induction - An Introduction With Chocolate Bars
Lecture 90 Using Strong Induction To Prove Statements About Chocolate Bars
Lecture 91 Using Strong Induction To Prove: Natural Numbers Factor Into Products Of Primes
Section 17: PART 3.6: SEQUENCES REVIEW WITH DETAILED SOLUTIONS
Section 18: PART 4.1: PROPOSITIONAL LOGIC - Determine Truth Values Of Molecular Statements
Lecture 92 An Introduction To Arguments and Propositions In Mathematics
Lecture 93 What Are Truth Tables - Interpreting Complex Statements With Truth Values
Lecture 94 What Is Logical Equivalence?
Lecture 95 What Are De Morgan's Laws?
Lecture 96 Using Truth Tables To Show How Implications Are Disjunctions
Lecture 97 The Negation Of The Negation Is Logically Equivalent To The Original
Lecture 98 What Does It Mean To Negate An Implication?
Lecture 99 Deductions - How To Deduce Within A Proof
Lecture 100 Let's Go Beyond Propositions
Section 19: PART 4.2: PROOFS AND PROVING TECHNIQUES - Overview Of Common Proving Techniques
Lecture 101 What Is A Proof In Discrete Math?
Lecture 102 The Proof That There Are Infinitely Many Primes
Lecture 103 How To Create A Direct Proof - Proving If n Is Even, Then n^2 Is Even
Lecture 104 Creating A Proof By Contrapositive With An Example
Lecture 105 Creating A Proof By Contradiction - Proving The Negative Of A Statement Is False
Lecture 106 Proof By Counterexample - How To Proving A Statement Is NOT True
Lecture 107 How To Use Cases To Prove Statements
Section 20: PART 4.3: SYMBOLIC LOGIC AND PROOFS REVIEW WITH DETAILED SOLUTIONS
Section 21: PART 5.1: GRAPH THEORY DEFINITIONS - An Introduction To Graph Theory
Lecture 108 Introduction To Graphs And Graph Theory
Lecture 109 What Is A Graph?
Lecture 110 What Are Isomorphic Graphs? What Does It Mean To Be Isomorphic In This Context?
Lecture 111 The Definition Of A Subgraph And An Induced Subgraph
Lecture 112 An Overview Of Simple Graphs, Multigraphs And Connected Graphs
Lecture 113 An Overview Of Complete Graphs And The Degree Of A Vertex
Lecture 114 The Handshaking Lemma With Examples
Lecture 115 Advanced Graphs: Bipartite Graphs And Complete Bipartite Graphs
Lecture 116 A Complete List Of Important Definitions In Graph Theory
Section 22: PART 5.1: TREES - Discover Many Various Properties And Algorithms Involving Tree
Lecture 117 What Are Trees And Why Are They Important?
Lecture 118 Properties Of Trees - Part One
Lecture 119 Properties Of Trees - Part Two
Lecture 120 Properties Of Trees - Part Three
Lecture 121 Breadth First Searches And Depth First Searches With Rooted Trees
Lecture 122 An Overview Of Rooted Trees
Lecture 123 What Are Spanning Trees?
Section 23: PART 5.2: PLANAR GRAPHS - Determine various properties using Euler's Formula
Lecture 124 An Introduction To Planar Graphs - Graphs That Don't Intersect Themselves
Lecture 125 What Is Euler's Formula For Planar Graphs
Lecture 126 The Complex Nature Of Non-planar Graphs
Lecture 127 Interpreting Polyhedra With Graph Theory
Section 24: PART 5.3: COLORING GRAPHS - Apply Various Coloring Schemes To Color Graphs
Lecture 128 A Look Into Coloring Graphs In General
Lecture 129 What Is The Four Color Theorem?
Lecture 130 Cliques And The Clique Number In Graph Theory
Lecture 131 An Introduction To Coloring Graphs - Brooks' Theorem
Lecture 132 Coloring Edges Of Graphs, Instead Of Vertices
Lecture 133 An Introduction To Ramsey Theory
Section 25: PART 5.4: EULER PATHS AND CIRCUITS - Understanding Special Paths And Cycles
Lecture 134 Euler Paths And Circuits In Graph Theory - Part One
Lecture 135 Euler Paths And Circuits In Graph Theory - Part Two
Lecture 136 Hamiltonian Paths - A Look Into Very Special Paths On Graphs
Section 26: PART 5.5: MATCHING IN BIPARTITE GRAPHS - Apply Concepts From Graph Theory
Lecture 137 An Introduction To Matching In Bipartite Graphs
Lecture 138 Understanding Hall's Marriage Theorem
Section 27: PART 5.6: GRAPH THEORY REVIEW WITH DETAILED SOLUTIONS
Section 28: PART 6 (EXTRA): GENERATING FUNCTIONS - Easily Solve Complex Recurrence Relations
Lecture 139 An Introduction To Generating Functions
Lecture 140 How To Create A Generating Function - Part One
Lecture 141 How To Create A Generating Function - Part Two
Lecture 142 What Is Differencing With Generating Functions?
Lecture 143 Multiplication And Partial Sums
Lecture 144 How To Solve Recurrence Relations With Generating Functions
Section 29: PART 7 (EXTRA): NUMBER THEORY - Study Patterns And Secrets Of Natural Numbers
Lecture 145 Introduction To Number Theory - My Favorite Math Topic!
Lecture 146 What Is Divisibility - Dividing versus Dividable
Lecture 147 A Formal Representation Of The Division Algorithm
Lecture 148 An Overview Of The Remainder Classes
Lecture 149 Introduction To The Congruence Modulo (mod n)
Lecture 150 What Are Properties Of Congruences In Number Theory?
Lecture 151 How To Properly Divide While Working With Congruences (mod n)
Lecture 152 How To Solve For Variables In Congruences
Lecture 153 Which Congruences Have No Solutions?
Lecture 154 A Complete Guide To Solving Linear Diophantine Equations Part One
Lecture 155 A Complete Guide To Solving Linear Diophantine Equations Part Two
Section 30: PART 8: CONCLUSION - HOW TO KEEP LEARNING
Lecture 156 Conclusion Lecture
Lecture 157 Bonus Lecture (Coupon Codes For Other Courses - Updated 6/30/20)
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
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Master Discrete Math 2020 More Than 5 Complete Courses In 1

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