[old stuff] SIM1001, SIX1013, SJEM1110 Basic Mathematics: Lecture notes, tutorial question etc etc.

SIM1001, SIX1013, SJEM1110 Basic Mathematics

*** Old stuff below ***

Lecture notes and tutorial questions. You may download them here.

Mid semester test 2 results:

You may view the results here

Mid semester test 1 results:

You may view the results here.

Mid semester test 2:

The details are as follows:

Date: Thursday, 10 December 2015
Time: 1130 - 1230 hrs
Venue: Level 1, Hall 3, B Wing, The New Examination Building

Topics examined: reduced row echelon form, system of linear equations, determinants, among other things.

Mid semester test 1:

The details are as follows:

    Date: Thursday, 5 November 2015

    Time: 1130 - 1230 hrs

    Venue: Lower Ground, Hall 1, B Wing, The New Examination Building

Chapters examined: Chapter 1 - Logic, Chapter 2 - Induction and Chapter 3 - Binomial Theorem

Write the answers on the question sheets.

Tutorial classes:

Update: Wednesday, 30 September 2015. Please choose the time most suitable to you for tutorial class. At the moment, I am opening 8 slots. I very much prefer to hold the tutorial sessions on Tuesdays and Thursdays.

You can always revise your choices. Suggestions are welcomed.

Lecture notes:

Update: Monday, 21 September 2015. 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


Update: Thursday, 22 October 2015. Linear Algebra notes. These are for the second part of this course. The notes are courtesy of Prof Wong Peng Choon.

We will use these notes in the lectures.

Tutorial questions

Update status

Update: Tuesday, 27 October 2015 - Solutions to Tutorial 6, Tutorial 7 and Tutorial 8 uploaded Update: Wednesday, 14 October 2015 - supplementary tutorial questions uploaded

Update: Wednesday, 14 October 2015 - Tutorial 6, Tutorial 7 and Tutorial 8 uploaded
Update: Wednesday, 14 October 2015 - Solutions to Tutorial 3, Tutorial 4 and Tutorial 5 uploaded.
Update: Tuesday, 6 October 2015 - Tutorial 4 and Tutorial 5 uploaded
Update: Thursday, 1 October 2015 - Solutions to Tutorial 1 and Tutorial 2 uploaded

Part I

Tutorial 1: questions on Logic, and solution

Tutorial 2: questions on Logic, and solution

Tutorial 3: question on Logic, Mathematical Induction and Binomial Theorem, and solution

Tutorial 4: questions on sets and relations, and solution

Tutorial 5: questions on relations and functions, and solution

Tutorial 6: questions on Complex numbers and solution

Tutorial 7: questions on Complex numbers and solution

Tutorial 8: questions on polynomials and solution

Part II (solutions to selected problems)

Tutorial 9: questions on echelon form, linear equations

    solution to Tutorial 9, Question 1

    solution to Tutorial 9, Question 3

    solution to Tutorial 9, Question 7(iii)

Tutorial 10: questions on symmetry, skew-symmetry

Tutorial 11: questions on matrix operations, inverse of a matrix

Tutorial 12: questions on determinant, Cramer's rule

Tutorial 13: questions on adjoint

Tutorial 14: questions on linear combinations, linear independence
 
    solution to Tutorial 14, Question 4 (i) and (ii)

    solution to Tutorial 14, Question 4 (iii) and (iv)

Tutorial 15: questions on characteristic polynomials, eigenvectors, eigenvalues, Cayley-Hamilton theorem

    solution to Tutorial 15, Question 4 (a) and (b)

    solution to Tutorial 15, Question 5

Answers to selected exam questions

Suppose an n x n matrix A has n distinct eigenvalues and B an n x n matrix such that AB = BA. Show that B is diagonalizable.

    Supplementary tutorial questions (solutions not available)

        Tutorial 1: questions on Logic
    
        Tutorial 2: questions on Logic
    
        Tutorial 3: questions on Logic, Mathematical Induction and Binomial Theorem

      Tutorial 4: questions on Sets and Relations

      Tutorial 5: question on Relations and Functions

      Tutorial 6: questions on Complex numbers

      Tutorial 7: questions on Complex numbers

      Tutorial 8: question on polynomials


      These notes are in Microsoft Word format, courtesy of Prof Wong Peng Choon.
        You should use the current notes which are an improved version of these notes.

        Chapter 6: Matrices, row echelon form (ref), reduced row echelon form (rref)

       Chapter 7: Systems of linear equations

       Chapter 8: Algebra of Matrices

       Chapter 9: Determinants

       Chapter 10: Linear combination, linear independence of vectors and rank of a matrix

       Chapter 11: Eigenvalues and Eigenvectors

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)