### Announcement/Reminder

• Quiz:
• Time: 1900-2100hrs, Thursday 26/10. Venue: LSK LT5.
• Supplementary Lecture:
• Time: 1830-2015hrs, Monday 09/10. Venue: LSB C3.
• Time: 1830-2015hrs, Wednesday 15/11. Venue: LSB C3.
• Final Examination:

### Time and Venue

• Lectures and tutorials: Mondays 1430-1615hrs LSB LT5, Wednesdays 1030-1215hrs LHC 104.

### Assessment Scheme

• Coursework: 50%
• Final Examination: 50%

For more details, please refer to the course information sheet.

### Supplementary Material

• Lecture outlines and handouts
• Lecture 1
• Handout: Mathematical statements and predicates
• Lecture 2
• Handout 1: Examples of simple inequalities justified using `direct proofs'
• Handout 2: `Direct proofs' for basic results on divisibility
• Handout 3: Examples of proofs of statements with conclusion `... iff ...'
• Handout 4: Important inequalities
• Lecture 3
• Handout 1: Examples of proofs-by-contradiction
• Handout 2: Basic results on complex numbers `beyond school mathematics'
• Lecture 4
• Lecture 5
• Handout 1: Principle of mathematical induction
• Handout 2: Examples of mathematical induction
• Lecture 6
• Handout 1: Basics of logic in mathematics
• Handout 2: Applications of logic in mathematics
• Lecture 7
• Handout 1: Examples of proofs concerned with `subset relations'
• Handout 2: Examples of proofs for properties of basic set operations
• Lecture 8
• Lecture 9
• Lecture 10 (Supplementary Lecture)
• Lecture 11
• Handout: Universal quantifier and existential quantifier
• Lecture 12
• Lecture 13
• Handout 1: Notion of functions and its pictorial visualizations
• Handout 2: Ordered pairs, ordered triples and cartesian products
• Lecture 14
• Handout 1: Surjectivity and injectivity
• Handout 2: Surjectivity and injectivity for `nice' real-valued functions of one real variable
• Handout 3: Surjectivity and injectivity for linear transformations
• Handout 4: Surjectivity and injectivity for `simple' complex-valued functions of one complex variable
• Lecture 15
• Lecture 16
• Handout 1: Image sets and pre-image sets
• Handout 2 (Sketch): Image sets and pre-image sets under `nice' real-valued functions of one real variable
• Handout 3: Parametrizations for curves and surfaces
• Handout 4: Curves and surfaces as level sets
• Handout 5a: Image sets and pre-image sets under linear transformations
• Handout 5b: Pictures for Handout 5a
• Lecture 17
• Handout: Compositions, surjectivity and injectivity
• Lecture 18
• Handout 1: Theoretical results involving image sets and pre-image sets
• Handout 2: Characterization of surjectivity with image sets, pre-image sets
• Lecture 19
• Handout 1: Notion of inverse functions
• Handout 2: Examples of bijective functions and their inverse functions
• Lecture 20
• Handout 1: Notion of function and `well-defined-ness'
• Handout 2: Existence and uniqueness of inverse functions
• Handout 3: Anthology on definitions for the notion of `function'
• Handout 4: Groups
• Lecture 21
• Handout: Relations
• Lecture 22 (Supplementary Lecture)
• Handout 1: Integers modulo n
• Handout 2: Basic `algebraic structures' with `addition' and `multiplication'
• Lecture 23
• Handout: Sets of equal cardinality
• Lecture 24
• Handout: Cantor's diagonal argument
• Lecture 25
• Handout 1: Sets of not necessarily the same size
• Handout 2: Proof of the Schroeder-Bernstein Theorem
• Lecture 26
• Handout 1: Cantor's Theorem and its consequences
• Handout 2: Zermelo-Fraenkel Axioms with the Axiom of Choice
• Handout 3: Finite sets versus infinite sets
• Handout 4: Proof of the characterizations of infinite sets
• Lecture 27
• Handout: Countable sets and uncountable sets
• Assignments
• Further Exercises
• Proof-type Exercises in calculus of one variable and linear algebra

### Quizzes

• Quiz (Solution)