# Edinburgh

F17CC Introduction to University Mathematics 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. 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.

Syllabus

Check out the syllabus for learning outcomes

 Week/dates Tuesday 11.20 Thursday 10.20 Friday 10.20 Homework Week 1 16th to 20th September 1. Combinatorics Lecture 1: introduction to the course Introduction to course 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

Assessment

 Tests 20% These are closed book tests for feedback. Test 1. Week 4.  Section 1. Test paper and solutions. 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. I am, however, required by my department to provide you with one past exam paper simply to show you the nature of the exam: 2019 Exam paper and solutions Highest mark = 100; average mark = 65 ; lowest mark = 4. THE LEARNING OUTCOMES IN THE SYLLABUS ARE EFFECTIVELY A LIST OF ALL POSSIBLE EXAM QUESTIONS. So, check out the syllabus above now. The actual 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:
Christina Lazaridou, Nikoletta Louca, Kieran Quaine

YOU WILL HAVE 1 TUTORIAL A WEEK in F17CC

Tutorials start in week 2

If your programme is not mentioned explicitly below

Maths students means all students on a Maths or a Maths and/with degree NOT AMS students

email me if there are work conflicts

 Time Who 13.20-14.10 AMS students: surnames A to J 14.20-15.10 AMS students: surnames K to Z 15.20-16.10 Maths Students: surnames A to K (except Maths with/and CS) All Maths with Finance students All MSAS students 16.20-17.10 Maths Students: surnames L to Z In addition, 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

HARD COPIES WILL NOT BE PROVIDED.

 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

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

M. V. Lawson, Algebra & Geometry: An introduction to university mathematics, CRC Press, 2016.
A PDF of a prepublication version of this book will be made freely available via VISION to all students registered for this course.
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.
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.

STEP QUESTIONS

If you want to really develop your mathematical skills you need to attempt much more thought-provoking questions than I provide in this course. I recommend the following website

https://maths.org/step/welcome

and, in particular, the Advanced Problems in Mathematics book. A free PDF is available here where you can also buy the book itself. Be warned that the questions cover much wider ground than is covered
in this course. In addition, I would recommend the books of A. Gardiner.

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.