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Discrete Mathematics - MATH 210

Covers logic, sets, functions, proof techniques, combinatorics, graph theory, recursion, and discrete structures.

Study Tools

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Study guides

12

03 Relations and Functions

A progressive guide to relations, their structural properties, and the ways functions can be classified and inverted.
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05 Induction and Recursion

A structured guide to proving statements about natural numbers and recursively generated objects, defining recursive functions and sets, and selecting the proof method that matches a construction.
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07 Advanced Counting Methods

A progressive guide to choosing and applying binomial coefficients, the binomial theorem, inclusion-exclusion, and recurrence relations in advanced counting problems.
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06 Fundamental Counting Principles

A progressive guide to counting finite outcomes using addition, multiplication, factorials, permutations, combinations, the pigeonhole principle, and restriction-based strategies.
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10 Trees and Graph Algorithms

A structured guide to graph foundations, tree properties, spanning trees, rooted representations, traversals, fundamental graph algorithms, and practical applications.
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04 Proof Techniques

A structured guide to selecting, organizing, and writing valid mathematical proofs, including direct proofs, contrapositives, contradiction, cases, counterexamples, and clear mathematical exposition.
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11 Graph Properties and Applications

A structured guide to using Eulerian and Hamiltonian structures, planarity, coloring, and matching theory to model and solve network, scheduling, routing, and assignment problems.
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08 Sequences and Recurrences

A structured guide to describing sequences, simplifying sums, modeling and solving recurrence relations, using generating functions, and analyzing recursive algorithms.
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09 Introduction to Graph Theory

A structured introduction to graph theory covering graph terminology, representations, degrees, routes, cycles, connectivity, and subgraphs.
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12 Discrete Structures and Algorithms

A progressive guide to Boolean logic, circuits, algorithm design and correctness, asymptotic analysis, and the foundations of computational complexity.
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02 Sets and Set Operations

A progressive guide to representing sets, comparing them, performing set operations, working with products and power sets, organizing indexed families, and proving set identities.
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01 Logic and Quantifiers

A structured guide to evaluating propositions, using logical connectives and truth tables, simplifying equivalent statements, and translating quantified English into formal logic.
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Quizzes

12

12 Discrete Structures and Algorithms

A medium-difficulty quiz on Boolean algebra, propositional circuits, algorithms, correctness proofs, asymptotic growth, and computational complexity. Questions progress from foundational application to integrated reasoning.
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06 Fundamental Counting Principles

A medium-difficulty quiz on the Fundamental Counting Principles, including addition and multiplication principles, factorials, permutations, combinations, pigeonhole arguments, and methods for handling counting restrictions.
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08 Sequences and Recurrences

A medium-difficulty quiz on sequences, summation techniques, recurrence relations, characteristic roots, generating functions, and recursive algorithms. Questions progress from foundational applications to more involved reasoning.
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07 Advanced Counting Methods

A medium-difficulty quiz on advanced counting methods, including binomial coefficients, stars and bars, the binomial theorem, inclusion-exclusion, recurrences, tilings, derangements, and characteristic equations.
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04 Proof Techniques

A medium-difficulty quiz on selecting, constructing, and evaluating mathematical proof techniques, counterexamples, and mathematical writing practices.
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02 Sets and Set Operations

A medium-difficulty quiz on sets, subsets, set operations, Cartesian products, power sets, indexed families, and set identities. Questions progress from introductory applications to more involved reasoning.
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09 Introduction to Graph Theory

A medium-difficulty quiz on fundamental graph-theory concepts, including graph structure, representations, degrees, paths, cycles, connectivity, components, and subgraphs.
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01 Logic and Quantifiers

A medium-level quiz on propositions, logical connectives, truth tables, equivalence, predicates, quantifiers, negation, and formal translation.
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05 Induction and Recursion

A 14-question quiz on mathematical induction, strong induction, well-ordering, recursive definitions, and structural induction. Questions progress from introductory recognition to medium-difficulty application and proof reasoning.
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10 Trees and Graph Algorithms

A medium-difficulty quiz on trees, spanning trees, rooted-tree terminology, traversals, and fundamental graph algorithms. Questions progress from foundational understanding to algorithm selection and explanation.
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11 Graph Properties and Applications

A medium-difficulty quiz on Eulerian and Hamiltonian structures, planarity, coloring, matchings, Hall’s theorem, and graph-theoretic modeling. Questions progress from theorem application to integrated problem solving.
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03 Relations and Functions

A medium-difficulty quiz on relations, relation properties, equivalence relations, partial orders, functions, injectivity, surjectivity, bijections, and inverse functions. The questions emphasize applying definitions to examples and interpreting mathematical structure.
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Flashcards

12

12 Discrete Structures and Algorithms

A focused review of Boolean logic, circuits, algorithms, correctness proofs, asymptotic growth, and computational complexity.
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09 Introduction to Graph Theory

A focused review of graph-theory terminology, representations, degrees, routes, cycles, connectivity, and subgraphs.
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04 Proof Techniques

A focused set of flashcards on selecting, structuring, and evaluating direct proofs, indirect proofs, cases, counterexamples, and mathematical writing.
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07 Advanced Counting Methods

A focused review of binomial coefficients, algebraic expansion, inclusion-exclusion, and recurrence-based counting methods.
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06 Fundamental Counting Principles

A focused set of flashcards covering fundamental counting principles, factorials, permutations, combinations, pigeonhole arguments, and methods for handling counting restrictions.
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03 Relations and Functions

Review the definitions, properties, classifications, and inverse relationships that connect relations and functions in discrete mathematics.
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10 Trees and Graph Algorithms

Review the defining properties of trees, spanning trees, rooted-tree structure, traversals, graph algorithms, and practical applications.
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05 Induction and Recursion

A focused review of mathematical induction, strong induction, well-ordering, recursive definitions, and structural induction for discrete mathematics.
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08 Sequences and Recurrences

A focused review of sequences, summation methods, recurrence relations, characteristic roots, generating functions, and recursive algorithms.
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11 Graph Properties and Applications

Review core graph properties, existence criteria, algorithms, and applications involving routes, tours, planar drawings, coloring, scheduling, and matching.
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02 Sets and Set Operations

A focused review of set notation, relationships, operations, products, power sets, indexed families, identities, and element-based proofs.
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01 Logic and Quantifiers

A focused set of flashcards covering propositions, connectives, truth tables, logical equivalence, predicates, quantifiers, negation, and formal translation.
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