Free Discrete Mathematics Video Lessons with Transcripts (4 College Credits) | UPI Study

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Discrete Mathematics: every lesson, free with a free account

13 chapters · 87 video lessons with full transcriptsMath 230 · 4 credits · recommended for credit by NCCRS

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Chapter 1Logic and Mathematical Proof

  1. 1.1 · 12 minWhat Is Logic and Why It Matters in Mathematics
  2. 1.2 · 12 minTypes of Logical Fallacies and How to Recognize Them
  3. 1.3 · 11 minPropositions, Truth Values, and Truth Tables
  4. 1.4 · 10 minLogical Connectives: AND, OR, NOT, and More
  5. 1.5 · 8 minConditional Statements: If-Then, Converse, Inverse, and Contrapositive
  6. 1.6 · 9 minLaws of Logic and Logical Equivalence
  7. 1.7 · 9 minWriting Direct Proofs
  8. 1.8 · 8 minTautologies and Contradictions

Chapter 2Set Theory and Functions

  1. 2.1 · 8 minSets and Set Notation
  2. 2.2 · 8 minThe Universal Set and Subsets
  3. 2.3 · 8 minSet Complement and Set Difference
  4. 2.4 · 9 minCardinality and Types of Subsets
  5. 2.5 · 8 minPartially Ordered Sets and Lattices
  6. 2.6 · 8 minFunctions: Definitions and Terminology
  7. 2.7 · 8 minInjective Functions: One-to-One Mappings and Their Properties
  8. 2.8 · 9 minSurjective and Bijective Functions

Chapter 3Sequences and Series

  1. 3.1 · 9 minIntroduction to Sequences
  2. 3.2 · 8 minFinite vs. Infinite Sequences
  3. 3.3 · 7 minArithmetic Sequences
  4. 3.4 · 10 minGeometric Sequences
  5. 3.5 · 10 minSigma Notation and Series
  6. 3.6 · 9 minSum of Arithmetic Series
  7. 3.7 · 9 minSum of Geometric Series
  8. 3.8 · 8 minPractice: Arithmetic and Geometric Series

Chapter 4Mathematical Induction

  1. 4.1 · 9 minPrinciples of Mathematical Induction
  2. 4.2 · 14 minConstructing Proofs by Induction

Chapter 5Counting Methods and Basic Probability

  1. 5.1 · 9 minCounting Outcomes and Sample Spaces
  2. 5.2 · 11 minThe Addition and Multiplication Rules
  3. 5.3 · 9 minThe Pigeonhole Principle
  4. 5.4 · 9 minPermutations and Ordered Arrangements
  5. 5.5 · 9 minProbability of Permutation Events
  6. 5.6 · 8 minCircular Permutations
  7. 5.7 · 9 minCombinations and Unordered Selections
  8. 5.8 · 7 minProbability of Combination Events

Chapter 6Random Variables and Expected Value

  1. 6.1 · 8 minRandom Variables in Discrete Probability
  2. 6.2 · 8 minExpected Value: Meaning and Calculation
  3. 6.3 · 8 minTheoretical Discrete Probability Distributions
  4. 6.4 · 8 minEmpirical Discrete Probability Distributions
  5. 6.5 · 10 minApplied Discrete Probability Problems

Chapter 7Probability in Games, Gambling, and Strategic Decision

  1. 7.1 · 11 minProbability in Dice Games
  2. 7.2 · 10 minProbability in Blackjack
  3. 7.3 · 11 minProbability of Poker Hands
  4. 7.4 · 9 minProbability of Low-Hand Poker Variants
  5. 7.5 · 8 minProbability and Expected Value in Lotteries
  6. 7.6 · 11 minComparing Game Strategies with Expected Value

Chapter 8Binomial Probability, Recurrence Relations, and Generating Functions

  1. 8.1 · 9 minBinomial Experiments and Their Conditions
  2. 8.2 · 8 minThe Binomial Probability Formula
  3. 8.3 · 8 minSolving Binomial Probability Problems
  4. 8.4 · coming soonUsing Binomial Probability Tables
  5. 8.5 · coming soonFinding the Mean of a Binomial Distribution
  6. 8.6 · 8 minMeasuring Spread in Binomial Distributions
  7. 8.7 · 8 minApplied Binomial Experiment Problems
  8. 8.8 · 9 minRecursive Functions and Self-Referential Definitions
  9. 8.9 · 9 minFirst-Order Linear Recurrence Relations
  10. 8.10 · coming soonSolving Linear Recurrence Relations
  11. 8.11 · 10 minRecurrences in Divide-and-Conquer Algorithms
  12. 8.12 · 11 minIntroduction to Generating Functions
  13. 8.13 · 8 minThe Inclusion-Exclusion Principle

Chapter 9Graph Theory: Foundations and Euler Paths

  1. 9.1 · 10 minGraphs: Vertices, Edges, and Basic Definitions
  2. 9.2 · 9 minGraph Terminology and Key Concepts
  3. 9.3 · 10 minTypes of Graphs and Their Properties
  4. 9.4 · 9 minGraph Isomorphism and Homomorphism
  5. 9.5 · 8 minEuler Paths and Circuits
  6. 9.6 · 8 minFleury's Algorithm
  7. 9.7 · 10 minEuler's Theorems: Degrees, Paths, and Circuits
  8. 9.8 · 8 minEulerizing a Graph

Chapter 10Graph Theory: Hamiltonian Circuits, Coloring, and Representations

  1. 10.1 · 13 minHamiltonian Paths and Circuits
  2. 10.2 · 11 minWeighted Graphs and the Traveling Salesman Problem
  3. 10.3 · 12 minGraph Coloring and Traversal
  4. 10.4 · 9 minAdjacency Matrix and List Representations

Chapter 11Trees, Spanning Trees, and Minimum Cost Networks

  1. 11.1 · 9 minTrees: Properties and Definitions
  2. 11.2 · 9 minTree Traversal Methods
  3. 11.3 · 8 minSorting with Trees: Benefits and Limitations
  4. 11.4 · 8 minSpanning Trees and Their Properties
  5. 11.5 · 8 minKruskal's Algorithm for Minimum Spanning Trees
  6. 11.6 · 8 minPrim's Algorithm for Minimum Spanning Trees

Chapter 12Matrices and Transformations

  1. 12.1 · 9 minIntroduction to Matrices
  2. 12.2 · 10 minMatrix Operations and Inverses
  3. 12.3 · 9 minRotation Matrices and Their Applications
  4. 12.4 · 10 minTranslation Matrices and Their Applications

Chapter 13Boolean Algebra and Logic Circuits

  1. 13.1 · 8 minFoundations of Boolean Logic
  2. 13.2 · 9 minBoolean Algebra: Laws and Properties
  3. 13.3 · 9 minBoolean Expressions and Logical Operators
  4. 13.4 · 10 minKarnaugh Maps
  5. 13.5 · 10 minThe Arithmetic Logic Unit (ALU)
  6. 13.6 · 8 minLogic Gate Design
  7. 13.7 · 9 minSimplifying Logic Circuits

FAQ

Questions about Discrete Mathematics

Is this Discrete Mathematics lesson free?
Yes, with a free UPI Study account. Every one of the 87 video lessons in Discrete Mathematics has its own page with the full transcript, free to read; a free account unlocks the videos. The practice quizzes, graded work and college credit come with the course.
How many college credits is Discrete Mathematics?
Discrete Mathematics (Math 230) carries a NCCRS credit recommendation for 4 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
How much does Discrete Mathematics cost and what is included?
$250, paid once, with lifetime access: all 87 video lessons, a practice quiz after each, the graded work and final exam, and an official transcript when you finish. Students who want several courses choose UPI Study PRO instead.
Which universities accept UPI Study credits?
UPI Study has signed partner agreements with universities such as Thomas Edison State University, University of the People and Charter Oak State College, and works with universities such as Penn State, SNHU and SUNY. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities. Use "Find my college" on this page to check yours.
Can I download the Discrete Mathematics syllabus?
Yes, the full syllabus is a free PDF download; it asks you to sign in with a free UPI Study account first.
How long does Discrete Mathematics take?
It is self-paced with no deadlines. The 87 lessons total about 13 hours of video; most students add reading and practice time and finish in a few weeks to a few months, on their own schedule.
Do I need a prerequisite first?
Chapter 1 starts from logic and proof, so a student who is comfortable with algebra is ready; no calculus is needed. UPI Study also offers College Algebra, Calculus 1 and Calculus 2 as separate courses.
How are the exams done?
Quizzes and assignments are online in the course. The final exam is taken online with proctoring; a person on the UPI Study team checks assignments, usually within two days.
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