MA1100: Fundamental Concepts of Mathematics
AY2012/2013, Semester 1, Lecturer: Victor Tan
Course Coverage:
1. Variables & Statements
2. Sets, Relations & Functions
3. Predicates & Quantifiers
4. Theorem, Definition & Proof
5. Divisibility & Quotient Remainder Theorem
6. Methods of Proving
7. Greatest Common Divisor & Euclidean Algorithm
8. Principle of Mathematical Induction
9. Set Relations & Element Method
10. Power Sets, Index Collection & Partition of Sets
11. Image, Inverse Image & Range
12. Injective, Surjective & Bijective Functions
13. Composite Functions
14. Cardinality & Countability
15. Reflexive, Symmetric, Transitive Relations
16. Equivalence Classes, Relations & Partitions
17. Congruence Modulo, Modular Arithmetic, Congruence Classes & Integer Modulo
This modules introduce the foundation of mathematics through algebra, number and set theory. The first part of the module focus on building a strong foundation in logic. It then follows with logical analysis of relationship between different types of statements. Statement types include converse, inverse, contrapositive, compound and conditional.
The next part of the module will introduce the core ideas of mathematics rigorously, namely, the theorem-definition-proof concept. This part starts of with review of mathematical induction and its variations, followed by other indirect methods of proving such as contrapositive, contradiction, constructive and non-constructive proofs. Many of the proving methods are demonstrated using theorems from number theory.
The last part of the module touch on basic set theory, and reintroduces set relations and functions in a more rigorous setting. It starts with the chasing-element method which is the primary method of proving in set theory. Image mapping, range and properties of functions are being discuss from the set theory perspective. More in-depth concepts on sets and numbers such as cardinality and countability and introduce towards the end. The last few chapters focus on properties of set relations as well as modular arithmetic.
Overall, this has been my favorite mathematics module so far, and it really introduces mathematics from its conception through its development. The coverage of the module is very wide and hence a lot of time has to be devoted into catching up with the topics. However, most of the topics were not covered in-depth, hence it is a relatively easy and but competitive module.
Workload: Moderate
Difficulty: Moderate
Grade: B
Course Coverage:
1. Variables & Statements
2. Sets, Relations & Functions
3. Predicates & Quantifiers
4. Theorem, Definition & Proof
5. Divisibility & Quotient Remainder Theorem
6. Methods of Proving
7. Greatest Common Divisor & Euclidean Algorithm
8. Principle of Mathematical Induction
9. Set Relations & Element Method
10. Power Sets, Index Collection & Partition of Sets
11. Image, Inverse Image & Range
12. Injective, Surjective & Bijective Functions
13. Composite Functions
14. Cardinality & Countability
15. Reflexive, Symmetric, Transitive Relations
16. Equivalence Classes, Relations & Partitions
17. Congruence Modulo, Modular Arithmetic, Congruence Classes & Integer Modulo
This modules introduce the foundation of mathematics through algebra, number and set theory. The first part of the module focus on building a strong foundation in logic. It then follows with logical analysis of relationship between different types of statements. Statement types include converse, inverse, contrapositive, compound and conditional.
The next part of the module will introduce the core ideas of mathematics rigorously, namely, the theorem-definition-proof concept. This part starts of with review of mathematical induction and its variations, followed by other indirect methods of proving such as contrapositive, contradiction, constructive and non-constructive proofs. Many of the proving methods are demonstrated using theorems from number theory.
The last part of the module touch on basic set theory, and reintroduces set relations and functions in a more rigorous setting. It starts with the chasing-element method which is the primary method of proving in set theory. Image mapping, range and properties of functions are being discuss from the set theory perspective. More in-depth concepts on sets and numbers such as cardinality and countability and introduce towards the end. The last few chapters focus on properties of set relations as well as modular arithmetic.
Overall, this has been my favorite mathematics module so far, and it really introduces mathematics from its conception through its development. The coverage of the module is very wide and hence a lot of time has to be devoted into catching up with the topics. However, most of the topics were not covered in-depth, hence it is a relatively easy and but competitive module.
Workload: Moderate
Difficulty: Moderate
Grade: B