Lecturer Prof Mark V Lawson
Room CM G12
Ext 3210
Email m.v.lawson[at]hw.ac.uk

1. Combinatorics. Sections 3.1,
3.2 (first page only) and 3.9. Main goal:
understand and use set notation. 6 lectures. 
2. Polynomials. Sections
4.2, 4.3 and 4.4; Chapter 6; Sections 7.1, 7.2, 7.3,
7.4, 7.5, 7.9. Main goal: understand the
nature of the roots of a polynomial including
complex ones. 10 lectures. 
3. Matrices. Chapter
8 omitting Section 8.7 and only the characteristic
polynomials and their eigenvalues from Section 8.6.
Main goal: solve systems of linear equations
using elementary row operations. 6 lectures. 
4. Vectors. Sections 9.1, 9.2, 9.3, 9.4. Main
goal: find the vector equations of lines and
planes. 5 lectures 
Proofs. Read Chapter 2 for
the idea of proofs. The lectures will deal mainly
with proof by induction: Section 3.8. 1
lecture. 
Week/dates 
Tuesday 11.20 
Thursday 10.20 
Friday 10.20 
Week 1 10 Sept to 14 Sept 

Lecture
2 
Do: Exercises 1 and 2 
Week 2 17 Sept to 21 Sept 
Lecture 4 
Lecture 5 
Summary 
Week 3 24 Sept to 28 Sept 
START OF SECTION 2: Polynomials Lecture 7 
Axioms of highschool algebra Lecture 8 
Do: Exercises 4 and 5. 
Week 4 1 Oct to 5 Oct 
Lecture
10 
Lecture
11

Test 1 Friday 5th Oct. During lecture Based entirely on material in Lectures 1 to 6 inclusive 
Week 5 8Oct to 12 Oct 
Lecture
12 
Lecture
13 
Do: Exercises 6, Questions 5, 6 and 7. Start Exercises 7. 
Week 6 15 Oct to 19 Oct 
Lecture
15 
Lecture
16 END OF SECTION 2 

Week 7 22 Oct to 26 Oct 
Lecture
18 Properties of matrix operations 
Lecture
19 

Week 8 29 Oct to 2 Nov 
Lecture
21 
Lecture
22 The characteristic polynomial (not examined this year) Do: Exercises 9 END OF SECTION 3 
Test 2 Friday 2nd Nov. During lecture Based entirely on material in Lectures 7 to 16 inclusive. 
Week 9 5 Nov to 9 Nov 
START OF SECTION 4: vectors It is essential to read Sections 9.1, 9.2, 9.3 and 9.4 of the book Lecture 23 
Lecture
24 
Lecture
25

Week 10 12 Nov to 16 Nov 
Lecture
26 
Lecture
27 END OF SECTION 4 
Test 2. Week 8. Test paper and solutions. 
The goal of this course is to develop an understanding of the ideas and methods of university mathematics that will form the foundation for your further studies, therefore past papers will not be made available for this course. 
Exam
Advice

Time 
Who
To be confirmed 
13.2014.10 
AMS
students surnames A to L 
14.2015.10 
AMS
students surnames M to Z 
15.2016.10 
Maths
students surnames A to J (but not Maths and/with CS) BUT All MSAS students 
16.2017.10 
Maths
Students surnames K to Z BUT All Maths with/and CS 
Exercises 1 Warm up exercises 
Exercises 2 Section 1 Basic set theory 
Exercises 3 Section 1 Basic counting 
QUIZ
1 
Exercises 4 Section 2 Basic algebra 
Exercises 5 Section 2 The Binomial theorem 
Exercises 6 Section 2 Complex numbers 
Exercises 7 Section 2 Polynomials 
Exercises 8 Section 3 Matrices 
Exercises 9 Section 3 Matrices 
Exercises 10 Section 4 Vectors 

QUIZ
2 Thought Provoking Questions Question
4 requires knowledge of greatest common divisors
. See Section 5.2 (not part of course).
Question 9 is a combination of material on page 326 and Ex 10.1 (not part of course). If you are interested in mathematics both questions are worth studying. Otherwise omit. 
Solutions 1 
Solutions 2 
Solutions 3 
Solutions 
Solutions 4  Solutions 5 
Solutions 6 
Solutions 7 
Solutions 8 
Solutions 9 
Solutions 10 
Solutions 11 
