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
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)
Lecture videos and jottings
You can use the vlc media player to watch the videos
Week 1Tuesday, 15 March 2022: video (27.7 MB) and jottingsThursday, 17 March 2022: video (134.3 MB) and jottings
Tuesday, 15 March 2022: video (27.7 MB) and jottings
Thursday, 17 March 2022: video (134.3 MB) and jottings
Week 2Tuesday, 22 March 2022: video (147.2 MB) and jottings on conditionals, tautology and contradictionThursday, 24 March 2022: video (114.4 MB) and jottings on algebra of propositions and predicate logic
Tuesday, 22 March 2022: video (147.2 MB) and jottings on conditionals, tautology and contradiction
Thursday, 24 March 2022: video (114.4 MB) and jottings on algebra of propositions and predicate logic
Week 3Tuesday, 29 March 2022: video (134.0 MB) and jottings on predicates, quantifiers and categorical propositionsThursday, 31 March 2022: video (183.1 MB) and jottings on arguments and rules of inference
Tuesday, 29 March 2022: video (134.0 MB) and jottings on predicates, quantifiers and categorical propositions
Thursday, 31 March 2022: video (183.1 MB) and jottings on arguments and rules of inference
Week 4Tuesday, 5 April 2022: video (136.4 MB) and jottings on rules of inferenceThursday, 7 April 2022: video (138.3 MB) and jottings on regular induction
Tuesday, 5 April 2022: video (136.4 MB) and jottings on rules of inference
Thursday, 7 April 2022: video (138.3 MB) and jottings on regular induction
Week 5Tuesday, 12 April 2022: video (143.8 MB) and jottings on strong inductionThursday, 14 April 2022: video (142.1 MB) and jottings on the binomial theorem
Tuesday, 12 April 2022: video (143.8 MB) and jottings on strong induction
Thursday, 14 April 2022: video (142.1 MB) and jottings on the binomial theorem
Week 6Tuesday, 19 April 2022: no lecture as it was a public holidayThursday, 21 April 2022: video (162.7 MB) and jottings on sets and introduction to relations
Week 7Tuesday, 26 April 2022: video (176.0 MB) and jottings on relations, reflexivity, symmetry and transitivityThursday, 28 April 2022: video (158.0 MB) and jottings on logic tutorial
Mid semester break, Saturday, 30 April - Sunday, 8 May 2022
Week 8Tuesday, 10 May 2022: video (135.6 MB) and jottings on relations and functionsThursday, 12 May 2022: video (152.4 MB) and jottings on one-to-one and onto functions
Week 9Tuesday, 17 May 2022: video (85.8 MB) and jottings on onto functions, one-to-one correspondenceThursday, 19 May 2022: video (158.6 MB) and jottings on recapitulation of one to one, onto functions, composition of functions
Week 6
Tuesday, 19 April 2022: no lecture as it was a public holiday
Thursday, 21 April 2022: video (162.7 MB) and jottings on sets and introduction to relations
Week 7
Tuesday, 26 April 2022: video (176.0 MB) and jottings on relations, reflexivity, symmetry and transitivity
Thursday, 28 April 2022: video (158.0 MB) and jottings on logic tutorial
Mid semester break, Saturday, 30 April - Sunday, 8 May 2022
Week 8
Tuesday, 10 May 2022: video (135.6 MB) and jottings on relations and functions
Thursday, 12 May 2022: video (152.4 MB) and jottings on one-to-one and onto functions
Week 9
Tuesday, 17 May 2022: video (85.8 MB) and jottings on onto functions, one-to-one correspondence
Thursday, 19 May 2022: video (158.6 MB) and jottings on recapitulation of one to one, onto functions, composition of functions
Week 10Tuesday, 24 May 2022: video (130.4 MB) and jottings on introduction to complex numbersThursday, 26 May 2022: video (152.9 MB) and jottings on De Moivre's theorem and roots of complex numbers
Week 11Tuesday, 31 May 2022: video (160.4 MB) and jottings on ref and rref, and elementary row operationsThursday, 2 June 2022: video (144.2 MB) and jottings on system of linear equations
Week 12Tuesday, 7 June 2022: video (157.4 MB) and jottings on determinants, finding determinants using elementary row operationsThursday, 9 June 2022: video (164.5 MB) and jottings on linear independence
Week 13Tuesday, 14 June 2022: video (152.2 MB) and jottings on eigenvectors, eigenvalues and diagonalizationThursday, 16 June 2022: video (163 MB) and jottings on determinants and linear independence of vectors
Week 14Tuesday, 21 June 2022: Test 2, therefore, no lectureThursday, 23 June 2022: video (140 MB) and jottings on tutorial questions on linear independence of vectors and eigenvalues, eigenvectors, and diagonalization
Week 10
Tuesday, 24 May 2022: video (130.4 MB) and jottings on introduction to complex numbers
Thursday, 26 May 2022: video (152.9 MB) and jottings on De Moivre's theorem and roots of complex numbers
Week 11
Tuesday, 31 May 2022: video (160.4 MB) and jottings on ref and rref, and elementary row operations
Thursday, 2 June 2022: video (144.2 MB) and jottings on system of linear equations
Week 12
Tuesday, 7 June 2022: video (157.4 MB) and jottings on determinants, finding determinants using elementary row operations
Thursday, 9 June 2022: video (164.5 MB) and jottings on linear independence
Week 13
Tuesday, 14 June 2022: video (152.2 MB) and jottings on eigenvectors, eigenvalues and diagonalization
Thursday, 16 June 2022: video (163 MB) and jottings on determinants and linear independence of vectors
Week 14
Tuesday, 21 June 2022: Test 2, therefore, no lecture
Thursday, 23 June 2022: video (140 MB) and jottings on tutorial questions on linear independence of vectors and eigenvalues, eigenvectors, and diagonalization
