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14 units · 35 lessons

Discrete Structures

Discrete Structures from the first idea to exam level: every lesson builds on the one before, with a worked example, a step-through diagram where it helps, a quick check and practice that adapts to what you know. Follows Rosen, Discrete Mathematics and Its Applications, 7th ed..

Discrete Structures at a glance

What does Discrete Structures cover?

Sets, Venn Diagrams & Identities, Relations, Properties of Relations, Composition & Closures, Equivalence & Partial Orders, Sequences & Summations, Propositional Logic, Logical Equivalences, Predicates & Quantifiers, Rules of Inference, Proof Methods and Induction. It follows Rosen, Discrete Mathematics and Its Applications, 7th ed..

How many lessons does the Discrete Structures course on Studious have?

14 units and 35 lessons, from "What a set is" to "Proving formulas and divisibility". Each lesson has a worked example, a quick check and practice that adapts to what you know, and many have step-by-step diagrams.

Course outline

  1. Unit 1 · Week 1

    Sets and their notation

    1. What a set is
    2. Subsets and the empty set
    3. Power sets
  2. Unit 2 · Weeks 1–2

    Set operations and Venn diagrams

    1. Union, intersection and difference
    2. Complements and Venn diagrams
  3. Unit 3 · Week 3

    Using Venn diagrams and set identities

    1. Counting with Venn diagrams
    2. Set identities
  4. Unit 4 · Weeks 4–5

    Relations

    1. Ordered pairs and Cartesian products
    2. Binary relations, domain and range
    3. Arrow diagrams, digraphs and matrices
  5. Unit 5 · Week 6

    Reflexive and symmetric relations

    1. Reflexive and irreflexive relations
    2. Symmetric, antisymmetric and asymmetric
  6. Unit 6 · Week 7

    Transitive relations and combining relations

    1. Transitive relations
    2. Combining and composing relations
  7. Unit 7 · Week 8

    Closures, equivalence and order

    1. Closures of relations
    2. Equivalence relations and classes
    3. Partial orderings
  8. Unit 8 · Week 8

    Sequences and summations

    1. Sequences
    2. Summation notation
  9. Unit 9 · Week 9

    Propositional logic

    1. Propositions and connectives
    2. Conditionals and biconditionals
    3. Truth tables and applications
  10. Unit 10 · Week 10

    Propositional equivalences

    1. Tautologies and contradictions
    2. Laws of logic
  11. Unit 11 · Weeks 10–11

    Predicates and quantifiers

    1. Predicates and quantifiers
    2. Negating quantifiers
    3. Nested quantifiers
  12. Unit 12 · Weeks 12–13

    Rules of inference

    1. Valid arguments and modus ponens
    2. The rules of inference
    3. Building an argument step by step
  13. Unit 13 · Weeks 14–15

    Introduction to proof

    1. Direct proof
    2. Contraposition and contradiction
    3. Counterexamples and proof by cases
  14. Unit 14 · Week 16

    Mathematical induction

    1. The idea of induction
    2. Proving formulas and divisibility

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