1. MATH10001 Mathematical Workshop Dr Louise Walker (Alan Turing 2.243) louise.walker@manchester.ac.uk Office hours: Thursdays, Fridays 10:30-11:30am Course materials at www.blackboard.manchester.ac.uk or www.maths.manchester.ac.uk/undergraduate/ ugstudies/units/2010-11/level1/MATH10001/ louise.walker@manchester.ac.ukwww.blackboard.manchester.ac.ukwww.maths.manchester.ac.uk/undergraduate/ ugstudies/units/2010-11/level1/MATH10001/

2. MATH10001 Mathematical Workshop 4 Projects Individual and group work Homework Project reports Group presentation In class test in week 12 100% coursework and test – no exam in January

3. Week 1Introduction to the Workshop Week 2Project 1 - Conic Sections Week 3Project 1 - Conic Sections Week 4Group presentations Week 5Project 2 - Groups Week 6Mid-semester break Week 7Project 2 - Groups Week 8Project 3 - Difference Equations Week 9Project 3 - Difference Equations Week 10 Project 4 - Graphs Week 11Project 4 - Graphs Week 12In class test

4. Assessment Each project report is worth 15%. There will be a marks for the correctness of the mathematics, marks for the quality and clarity of presentation and a group mark. The group mark is 1/4 average mark for your group (only for those students who have attended the classes). Group presentation is worth 5%. In class test is worth 35%.

5. Working in groups For the projects and presentation you’ll be in group with 5 or 6 other students. Group times and rooms are given on the MATH10001 website. You’ll be working with a postgraduate facilitator. Working effectively with other people is a very useful skill.

6. Writing Mathematics maths is often poorly communicated who are you writing for? write in sentences use a suitable balance of words and symbols use diagrams and examples

7. Word processing mathematics There are several packages that can be used to produce mathematical text. Most professional mathematicians use LaTeX. To find out more see the online course at http://www.maths.manchester.ac.uk/~ahazel/courses_latex. html Or you can use Microsoft Word. This has an in-built Equation Editor that can be used to construct mathematical expressions. See the MATH10001 website for more details.

8. Thinking Mathematically Entry Attack Review (J. Mason – Thinking Mathematically)

9. Entry: Read and understand Use examples and diagrams Look for patterns

10. Attack: Generalise from specific examples Make conjectures Use logical arguments to prove conjectures Convince yourself, convince a friend, convince an enemy

11. Review: Check your working Have you covered all cases? Can you extend your arguments to other cases?

12. Which natural numbers x, y and z satisfy x 2 + y 2 = z 2 ? What about x 3 + y 3 = z 3 ? Some problems that are very easy to state still haven’t been solved. Goldbach’s Conjecture: Every even number greater than 2 can be written as the sum of two primes. 4=2+2, 6=3+3, 8=3+5, 10=5+5, 12 = 5+7, 14=7+7, 16=3+13, …

13. Group presentations Week 4 (Tuesday 19th October) 15 minute group presentation Famous mathematician life and works Each group produces a word processed handout to accompany the talk Assessed by your postgraduate facilitator