Autumn 2017

Edinburgh

F17CC Introduction to University Mathematics


Advice to reader


Lecturer
Prof Mark V Lawson


Room CM G12

Ext 3210

Email m.v.lawson[at]hw.ac.uk




Lectures
A draft of my book has been made available on VISION

Errata page for book here



Background reading: Chapters 1 and 2.
1. Combinatorics. Sections 3.1, 3.2 (first page only) and 3.9. Main goal: understand and use set notation.
2. Algebra: complex numbers and 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.
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 EROs.
4. Vectors. Sections 9.1, 9.2, 9.3, 9.4. Main goal: find the vector equations of lines and planes.

In conclusion: everything you wanted to know about proofs but were afraid to ask (see book for more information on proofs).


Syllabus


 Week/dates
Tuesday 11.15
Thursday 10.15
Friday 10.15
Week 1
11 Sept to15 Sept
BEGINNING OF SECTION 1

1. Lecture 1

2. Lecture 2
3. Lecture 3

You should attempt
Exercises 1 and 2

Week 2
18 Sept to 22 Sept
4. Lecture 4
5. Lecture 5
6. Lecture 6

You should attempt
Exercises 3 and Quiz 1

END OF SECTION 1
Week 3
25 Sept to 29 Sept
BEGINNING OF SECTION 2

7. Lecture 7
 No (physical) lecture. I am attending a PhD jury in Sweden (Uppsala).
HOWEVER, please ensure you read through the lecture notes above.
You need to understand the method of completing the square and what is meant by
an irreducible quadratic. See Section 4.3 of the book.
8. Lecture 8

9. Lecture 9

You should attempt
Exercises 4 and 5.
Week 4
2 Oct to 6 Oct
10. Lecture 10
11.  Lecture 11
12.  Lecture 12
You should attempt
Exercises 6

Week 5
9 Oct to 13 Oct
13.Lecture 13
14. Lecture 14
15. Lecture 15
You should attempt
Exercises 7
END OF SECTION 2
Week 6
16 Oct to 20 Oct
16. BEGINNING OF SECTION 3
Lecture 16

17. Lecture 17
18. Lecture 18
You should attempt
Exercises 8
Week 7
23 Oct to 27 Oct
19. Lecture 19
20. Lecture 20
21. Lecture 21
You should attempt
Exercises 9
HOMEWORK 1 DUE!
Week 8
30 Oct to 3 Nov
22. Lecture 22

 END OF SECTION 3
BEGINNING OF SECTION 4
23. Lecture 23
24. Lecture 24
You should attempt
Exercises 10
Week 9
6 Nov to 10 Nov
25. Lecture 25
26. Lecture 26

END OF SECTION 4
27. Lecture 27

Proofs
You should attempt
Exercises 11
HOMEWORK 2 DUE!
Week 10
13 Nov to 17 Nov
28. Lecture 28

Proofs
29. Lecture 29

Proofs

FIN

30.    Catch up on all exercises
Week 11
20 Nov to 24 Nov


 LAST TUTORIAL





Assessment

Homeworks 20%
Homework 1.

Solutions to homework 1.

Homework 2.

Solutions to homework 2



Final Exam 80%

2017 final exam

This has sketch solutions only. For details, see lecture notes.
Note that in Question 1(d) I also allowed induction.
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.

The exam will consist of questions which are of the same type as the tutorial questions as well as proofs from the lectures, exercise sheets and homeworks.
I will also expect you to know definitions and the statements of theorems.

All students are individually responsible for finding out when and where their exams are.



Exam Advice

1. READ each question thoroughly to ensure that you answer all parts of the question and that you have interpreted the question correctly.

2. COMMUNICATE your answers. Your solutions must be CLEAR and SELF-EXPLANATORY not written in an ideolect that only you know or adorned with hieroglyphics that only you can interpret. It is NOT the job of the marker to figure out what you meant or to detect the correct solutions amongst a sea of calculations. COMMUNICATION is not talking to yourself but expressing yourself to others.

3. CHECK your answers. This means checking that your solution answers the question originally posed. Do NOT ASSUME that your calculations are correct; do NOT ASSUME you have not made any mistakes. Your default position should be --- I might have made an error. If you find an error CORRECT IT.



Tutorials are on Thursday afternoons
Teaching assistants
Calum Ross, Lennart Schmidt, Spyridoula Sklaveniti


Tutorials start in week 2

If your programme is not mentioned explicitly below
please go to the tutorial given in your timetable


Maths students means all students on a Maths or a Maths and/with degree


Time
Who
1.15 to 2.15
AMS students surnames A to L
2.15 to 3.15
AMS students surnames M to Z
3.15 to 4.15
Maths students surnames A to L
(but not F181)

BUT
All MSAS students
4.15 to 5.15
Maths Students surnames M to Z
BUT
All F181 Maths with/and CS



Remember: the final exam paper will be closely based on questions selected from the exercise sheets below


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
Exercises 11
Section 4
Vectors

    

QUIZ 2

Thought
Provoking
Questions



Solutions 1

Solutions 2
Solutions 3
Solutions

Solutions 4 Solutions 5
Solutions 6

Solutions 7

Solutions 8
Solutions 9

Solutions 10

Solutions 11


You can find the solutions

to these questions
in the solutions to
the book exercises on VISION



Further reading and additional exercises

R. Hammack, Book of proof, VCU Mathematics Textbook Series, 2009. This book can be downloaded for free here.

J. Olive, Maths: a student's survival guide, second edition, CUP, 2006.

S. Lipschutz and M. Lipson, Discrete mathematics, revised third edition and onwards, Schaum's Outlines, McGraw-Hill Education, 2009.

S. Lipschutz and M. Lipson, Linear Algebra, fifth edition, Schaum's Outlines, McGraw-Hill Education, 2013.

C. McGregor, J. Nimmo, W. Sothers, Fundamentals of university mathematics, 3rd Revised Edition,  Woodhead Publishing Ltd, 2010.


Useful links
Numberphile

Centre for Innovation in Mathematics Teaching 
University of Plymouth

Online maths calculator
This is a nice multi-purpose site by Milos Petrovic.
You can check many of the calculations covered in my course via this site.

Online matrix calculator

Another online matrix calculator

An online version of Book 1 of Euclid's Elements

The MacTutor history of mathematics

A history of calculating

Understanding math(s)  
Excellent advice on learning and understanding mathematics by Peter Alfeld at the University of Utah.