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MathematicsYear 1Quality review 0/4

Mathematics — Year 1

A university first-year foundation in mathematics for South African students: single-variable calculus, linear algebra, discrete mathematics and probability. Every idea arrives in two modes — rigorous Theory and intuition-first Visual — with worked examples grounded in everyday South African life and practice problems that climb from routine to demanding.

≈ 12 h 30 min8 sections · 32 lessonsNo ratings yet
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What you'll learn

  • Evaluate limits and derivatives, apply the product, quotient and chain rules, and compute definite integrals using the Fundamental Theorem of Calculus
  • Perform vector and matrix operations, solve systems of linear equations by elimination, and use the determinant to decide invertibility
  • Reason with propositional logic, quantifiers and sets, and construct proofs by direct argument, contradiction and mathematical induction
  • Model uncertainty with probability, compute conditional probabilities and expected values, and summarise data with measures of centre and spread

Before you start

  • Grade 12 algebra and functions: manipulate polynomials, exponents and functional notation fluently
  • Introductory calculus from Grade 12: limits and the derivative of a polynomial from first principles
  • FET-phase probability and coordinate geometry: basic probability, the Cartesian plane and straight lines

Academic references

Use the latest available edition and your institution's prescribed text.

  • OpenStax, Calculus, Volumes 1–3
  • Gilbert Strang, Introduction to Linear Algebra
  • Daniel J. Velleman, How to Prove It

Formal work standard

  • State definitions and hypotheses before using a theorem.
  • Separate proof, counterexample, and numerical evidence.
  • Complete the problem sheet without solution steps before reviewing errors.

Course content

0/32 lessons
1. Calculus I: Limits, Derivatives and Integrals4 lessons
  1. Limits and ContinuityLesson25 min
  2. The Derivative from First PrinciplesLesson25 min
  3. Product, Quotient and Chain RulesLesson25 min
  4. Antiderivatives and the Definite IntegralLesson25 min
2. Linear Algebra I: Vectors, Matrices and Systems4 lessons
  1. Vectors in the Plane and SpaceLesson20 min
  2. Matrix OperationsLesson20 min
  3. Solving Systems by EliminationLesson25 min
  4. Determinants and InvertibilityLesson20 min
3. Discrete Mathematics: Logic, Sets and Proof4 lessons
  1. Propositional LogicLesson20 min
  2. Sets and Set OperationsLesson20 min
  3. Predicates and QuantifiersLesson20 min
  4. Proof TechniquesLesson25 min
4. Probability & Statistics I4 lessons
  1. Describing Data: Centre and SpreadLesson20 min
  2. Probability BasicsLesson20 min
  3. Conditional Probability and IndependenceLesson20 min
  4. Random Variables and ExpectationLesson20 min
5. Calculus I: Rigour and Applications6 lessons
  1. One-Sided and Infinite LimitsLesson25 min
  2. Continuity and the Intermediate Value TheoremLesson25 min
  3. Related RatesLesson25 min
  4. Optimisation with ConstraintsLesson25 min
  5. Integration by SubstitutionLesson25 min
  6. The Fundamental Theorem in ApplicationsLesson25 min
6. Linear Algebra I: Structure and Transformations4 lessons
  1. Span, Basis and DimensionLesson25 min
  2. Linear Transformations and MatricesLesson25 min
  3. Rank, Nullity and Solution StructureLesson25 min
  4. Least Squares and Orthogonal ProjectionLesson25 min
7. Discrete Mathematics: Counting and Relations3 lessons
  1. Mathematical InductionLesson25 min
  2. Counting and Binomial CoefficientsLesson25 min
  3. Relations and Equivalence ClassesLesson25 min
8. Probability and Statistics I: Models and Inference3 lessons
  1. Bernoulli and Binomial DistributionsLesson25 min
  2. Bayes' TheoremLesson25 min
  3. Sampling Variability and Confidence IntervalsLesson25 min