(current) Basic Math semester 2, session 2022/2023

Course title: Basic Mathematics

Course code: SIM1001/ SIX1013

 

Telegram group

 

Please join the group at: https://t.me/+b38__ZKmnIFhZWJi

Any announcement on lecture/tutorial reschedule, cancellation, etc. will be communicated via this group.

 

Microsoft Teams group

Please join the group at:

https://teams.microsoft.com/l/team/19%3aDE7LAMEWYdDhlSbjfBIkgWKR5zRc7LC95WjAZwTzvJY1%40thread.tacv2/conversations?groupId=6b978d73-4265-471f-b68b-4a6b98d0ed27&tenantId=a63bb1a9-48c2-448b-8693-3317b00ca7fb

 

The Team code is: vwrzret

 

Lecture schedules

 

Lectures are on:

    Mondays, 11-1 in BTM1

    Wednesdays, 11-1 in BTM1

 

 

Lecture notes

Part 1 of the course - Latest notes which contains Chapter 1: Logic, Chapter 2: Mathematical Induction, Chapter 3: Binomial Theorem, Chapter 4: Set Theory and Functions, Chapter 5: Complex numbers, Chapter 6: Polynomials

Supplementary notes on techniques for proof writing. The notes are extracted from the archive at Mathematics at Dartmouth.

Part 2 of the course: Notes on Part 2 of the course, Linear Algebra

Lecture jottings

 

Week 1:

13 March 2023: course briefing, a very short introduction to inductive, deductive arguments, valid/ invalid, sound/ unsound arguments

15 March 2023: conjunction, disjunction, negation, conditionals 

 

Week 2:

20 March 2023: conditionals, biconditionals, sufficient and necessary conditions, tautology and contradiction 

22 March 2023: logical equivalence, algebra of propositions

 

Week 3:

27 March 2023: predicate, universal and existential quantifiers, categorical propositions

29 March 2023: rules of inference  

 

Week 4:

3 April 2023: tutorial 2, rules of inference

5 April 2023: the principle of regular induction

 

Week 5:

10 April 2023: the binomial theorem, introduction to set, subset of a set  

12 April 2023: equality of sets, Cartesian product of sets, relations

Week 6:

17 April 2023: equivalence relations

19 April 2023: some exercises on relations

 

 

Mid semester break: 24 - 30 April 2023

Week 7:

1 May 2023: Labour Day

3 May 2023: mid semester Test 1

Week 8:

8 May 2023: relations and functions, one-to-one functions

10 May 2023: one-to-one, onto, and invertible functions

 

Week 9:

15 May 2023: lecture was postponed  

17 May 2023: introduction to polynomials, the division algorithm

 

Week 10:

22 May 2023: the division algorithm, the remainder theorem, the synthetic division 

24 May 2023: the factor theorem, roots and multiplicities

 

Week 11:

29 May 2023: +reduced row echelon form, elementary row operations

30 May 2023: system of linear equations, consistent and inconsistent system

 

Week 12:

5 June 2023: public holiday, no lecture

7 June 2023: symmetric, skew-symmetric matrices, linear combination, linear independence 

 

Week 13:

12 June 2023: linear independence and linear dependence, conceptual examples

14 June 2023: eigenvalues and eigenvectors 

 

Week 14:

19 June 2023: worked example on eigenvalues and eigenvectors

 

Tutorial questions

 

Part 1 - Algebra

 

Tutorial 1: questions on Logic and solutions

                  updated solution to tutorial 1, question 5a

Tutorial 2: questions on Logic and solutions

                  updated solution to tutorial 2, question 3(1a)

Tutorial 3: question on Logic, Mathematical Induction and Binomial Theorem and solutions
Tutorial 4: question on sets and relations and solutions
Tutorial 5: questions on relations and functions and solutions
Tutorial 6: questions on complex numbers and solutions
Tutorial 7: questions on complex numbers and solutions
Tutorial 8: questions on polynomials and solutions

Proof of the law of syllogism and correction

Part 2 - Linear Algebra

Tutorial 1: questions on matrices and system of linear equations and solutions
Tutorial 2: questions on symmetric and skew-symmetric matrices and selected solutions
Tutorial 3: questions on invertibility and product of matrices and solutions to selected problems and solution to question 9a
Tutorial 4: questions on determinant and solutions to selected problems
Tutorial 5: questions on adjoint and solutions to selected problems
Tutorial 6: questions on linear independence of vectors and solutions to selected questions
Tutorial 7: questions on eigenvalues and eigenvectors and solutions to selected question

Recommended references

Epp, Susanna. Discrete Mathematics with applications, Cengage Learning, 4th edition (2011)

Devlin, K. Sets, Functions and Logic. Chapman & Hall, 2nd edition (1992)

Larson, R. Elementary Linear Algebra. Brooks-Cole Cengage Learning, 7th edition (2013)

(older textbook) Larson, R and Falvo, D. Elementary Linear Algebra. Brooks-Cole Cengage Learning, 6th edition (2010)

Anton, H. and Rorres, C. Elementary Linear Algebra. Wiley, 11th edition (2014)

Supplementary references

Cuoco, Rotman. Learning Modern Algebra. AMS

Ulrich Daepp, Pamela Garkin. Reading, Writing and Proving - A closer look at Mathematics. Springer, Undergraduate Texts in Mathematics (2003)