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:
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:
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:
24 May 2023: the factor theorem, roots and multiplicities
Week 11:
29 May 2023: +reduced row echelon form, elementary row operations
Week 12:
5 June 2023: public holiday, no lecture
Week 13:
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
Tutorial 2: questions on Logic and solutions
Tutorial 2: questions on Logic and solutions
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)
Epp, Susanna. Discrete Mathematics with applications, Cengage Learning, 4th edition (2011)
(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)
Ulrich Daepp, Pamela Garkin. Reading, Writing and Proving - A closer look at Mathematics. Springer, Undergraduate Texts in Mathematics (2003)
