MTH 2122 units200 LevelFirst Semester

Sets, Logic and Algebra

B.Sc. Data Science, University of Uyo

Rigorous foundations: set theory, formal logic, relations and functions, and an introduction to abstract algebraic structures. This is where mathematical proof is taught properly, and where the language of the rest of your theoretical courses is set.

On Areté, MTH 212 comes with

  • 2 recommended textbooks
  • an AI tutor that has read this course’s outline and notes
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Course outline

  1. 01Set theory: operations, laws, power sets, Cartesian products, indexed families
  2. 02Propositional logic: connectives, truth tables, tautologies, logical equivalence
  3. 03Predicate logic: quantifiers, bound and free variables, negation of quantified statements
  4. 04Methods of proof: direct proof, contraposition, contradiction, mathematical induction
  5. 05Relations: reflexive, symmetric, transitive; equivalence relations and partitions
  6. 06Partial orders, Hasse diagrams and lattices
  7. 07Functions: injective, surjective, bijective; composition and inverse functions; cardinality
  8. 08Binary operations and algebraic structures: groups, subgroups, cyclic groups
  9. 09Rings and fields: definitions, examples and elementary properties

Recommended textbooks

  • Discrete Mathematics and Its Applications — Kenneth H. Rosen

    8th ed. — the standard text; superb exercise sets

  • Book of Proof — Richard Hammack

    3rd ed. — free at richardhammack.github.io; the clearest proof primer available

How to pass MTH 212

  • Proof is a skill, not knowledge — you must write proofs yourself, badly at first, to learn it. Reading proofs feels productive and is not
  • Equivalence relations and partitions are the mathematical basis of clustering: a clustering is literally a partition of your dataset
  • Learn to negate a quantified statement mechanically (¬∀x P(x) ≡ ∃x ¬P(x)) — it is examined and it is how you state a null hypothesis correctly
  • Hammack's Book of Proof is free and will teach you more in three chapters than a term of passive lectures

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