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. 7 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. 7 lectures. 
4. Vectors. Sections 9.1, 9.2, 9.3, 9.4. Main
goal: find the vector equations of lines and
planes. 4 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 
Homework 
Week 1 16th to 20th September 
Lecture
2 
Lecture
3 
Do Exercises
1. They only require school maths 

Week 2 23rd to 27th September 
Lecture
4 
Lecture
5 
Lecture
6 
Do Exercises
2. Do Exercises 3. Do Quiz 1. 
Week 3 30th September to 4th October 
Lecture 7 REVISION OF SECTION 1 END OF SECTION 1 
2. Polynomials Lecture 8 
Lecture
9 
Ensure
that you can do all 10 questions of Lecture 7. Exercises 4. 
Week 4 7th October to 11th October 
Lecture
10 
Lecture
11 
TEST 1 DURING LECTURE Section 1 only Test lasts 15 minutes You can stay as long as you like after that to complete it 
Exercises
5. Exercises 6. 
Week 5 14th October to 18th October 
Lecture
12 
Lecture
13 
Lecture
14 
Exercises
7. 
Week 6 21st October to 25th October 
Lecture
15 
Lecture
16 
Lecture
17 REVISION OF SECTION 2 END OF SECTION 2 
Complete all questions in Lecture 17. 
Week 7 28th October to 1st November 
3. Matrices Lecture 18 
Lecture
19 
Lecture
20 
Exercises
8. 
Week 8 4th November to 8th November 
Lecture
21 
Lecture
22 
TEST 2 DURING LECTURE
Section 2 only Test lasts 15 minutes You can stay as long as you like after that to complete it 
Exercises
9. 
Week 9 11th November to 15th November 
Lecture
23 
Lecture
24 Revision questions at end of lecture notes END OF SECTION 3 
4. Vectors Lecture 25 Geometric introduction to free vectors: vector addition, multiplication by a scalar, inner products and vector products. 
Exercises
10. 
Week 10 18th November to 22nd November 
Lecture
26 
Lecture
27 
Lecture
28 END OF SECTION 4 
Exercises
11. Exercises 12. 
Week
11 25th November to 29th November 
Lecture
29 Proof by induction 
LECTURES ARE CONCLUDED 
Tests 20%
These are closed book tests for feedback.
Test 2. Week 8. Section 2. Test paper and solutions. 
Final
Exam 80%
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. 
Exam
Advice

Time 
Who

13.2014.10 
AMS
students: surnames A to J 
14.2015.10 
AMS
students: surnames K to Z 
15.2016.10 
Maths
Students: surnames A to K (except Maths with/and CS) All Maths with Finance students All MSAS students 
16.2017.10 
Maths
Students: surnames L to Z In addition, 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 

A PDF of a prepublication version of this book will be made freely available via VISION to all students registered for this course.S. Lipschutz and M. Lipson, Discrete mathematics, revised third edition and onwards, Schaum's Outlines, McGrawHill Education, 2009.
The book covers much more than the lecture course but I have made clear above the sections you need. The errata page for this book
can be found here.