Autumn 2018

Edinburgh

F17CC Introduction to University Mathematics
Open Office: Thursday afternoons 15th, 22nd, 29th November


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. 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.



Syllabus


 Week/dates
Tuesday 11.20
 Thursday 10.20
Friday 10.20
Week 1
10 Sept to 14 Sept

START OF SECTION 1: Combinatorics


Lecture 1


Lecture 2
Do: Exercises 1 and 2
Read: Prolegomena, Chapter 1,  Section 3.1
and the first page of Section 3.2
Week 2
17 Sept to 21 Sept
Lecture 4

Lecture 5
Summary

Do: Exercises 3 and Quiz 1.

Read: Section 3.4, Section 3.9 and Section 4.1
(there is much, much more here than is in the course).
The course is defined by the Exercises below


END OF SECTION 1
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.
Read: Sections 4.2, 4.3 and 4.4.
Read Section 4.6 for interest (not part of this course)



Week 4
1 Oct to 5 Oct
Lecture 10
Lecture 11

Read: Section 6.1.
Do: Exercises 6, Questions 1 to 4.

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.
Read: Sections 6.1, 6.2, 6.3 and 6.4.
Read: Sections 7.1, 7.2, 7.3, 7.4, and 7.5.
(Spread all this reading over this week and next).


Week 6
15 Oct to 19 Oct
Lecture 15
Lecture 16

END OF SECTION 2

START OF SECTION 3: Matrices
 



Do: complete Exercises 7.

Read: the life of Evariste Galois.
For example, via the MacTutor link below.
For more on radical expressions (not politics),
see Section 7.5 and Section 7.9 of book.
Section 7.9 is for cultural enrichment and not part of the
course proper.

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

Lecture 19

Do: Exercises 8


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

Do: Exercises 10
Week 10
12 Nov to 16 Nov
Lecture 26
Lecture 27

END OF SECTION 4
PROOFS

Lecture 28

Do:Exercises 11
LECTURES END



Assessment

Tests 20%

These are closed book tests for feedback.

Test 1. Week 4. Test paper and solutions.
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.

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 tests.
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: Gissell Estrada,
Nikoletta Louca and Calum Ross

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

PLEASE ATTEND THE CORRECT SESSION:
email me if there are work conflicts

Time
Who
To be confirmed
13.20-14.10
AMS students surnames A to L
14.20-15.10
AMS students surnames M to Z
15.20-16.10
Maths students surnames A to J
(but not Maths and/with CS)
BUT
All MSAS students
16.20-17.10
Maths Students surnames K to Z
BUT
All Maths with/and CS



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

ALL QUESTIONS MUST BE ATTEMPTED WITHOUT LOOKING AT THE SOLUTIONS --- NOT EVEN FOR HINTS


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

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


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.