The course aims to provide a bridge between school and university (mainly, non-calculus) mathematics.
It will provide an introduction to the culture of mathematics including discussions of history, modern applications and the nature of reasoning, problem-solving and proofs.
In addition, basic skills will be developed in elementary combinatorics, complex numbers and polynomials, the algebra of matrices and their applications and geometry and vectors.
1.1 1. Propositional logic, 1.2 2. Compound propositions and truth tables, 1.3 3. Equivalence of propositions
2.1 1. Set theory notation, 2.2 2. Subsets and equality, 2.3 3. Intersection and union of sets, 2.4 4. Complement of sets
3. Mathematical Proof (3.1 1. Direct proofs, 3.2 2. Contrapositive proof, 3.3 3. Proof by contradiction, 3.4 4. Proof by induction)
4. Counting (4.1 1. The multiplication principle, 4.2 2. Addition and subtraction principles, 4.3 3. Factorials and permutations, 4.4 4. Counting subsets)
5. Complex Numbers (5.1 1. Addition, subtraction, multiplication and division of complex numbers, 5.2 2. Argand diagram, 5.3 3. Polar form of complex numbers, 5.4 4. De Moivre's theorem and Euler's identity, 5.5 5. Complex roots)
By the end of the course, students should be able to do the following:
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SCQF Level: 7
Credits: 15