Transcript MATH10001 Mathematical Workshop Dr Louise Walker (Alan Turing 2.243)

MATH10001
Mathematical Workshop
Dr Louise Walker
(Alan Turing 2.243)
[email protected]
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/
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
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Introduction to the Workshop
Project 1 - Conic Sections
Project 1 - Conic Sections
Group presentations
Project 2 - Groups
Mid-semester break
Project 2 - Groups
Project 3 - Difference Equations
Project 3 - Difference Equations
Project 4 - Graphs
Project 4 - Graphs
In class test
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%.
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.
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
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.
Thinking Mathematically
• Entry
• Attack
• Review
(J. Mason – Thinking Mathematically)
Entry:
• Read and understand
• Use examples and diagrams
• Look for patterns
Attack:
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Generalise from specific examples
Make conjectures
Use logical arguments to prove conjectures
Convince yourself, convince a friend,
convince an enemy
Review:
• Check your working
• Have you covered all cases?
• Can you extend your arguments
to other cases?
Which natural numbers x, y and z satisfy
x2 + y2 = z2 ?
What about
x3 + y3 = z3 ?
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, …
Group presentations
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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