|
|
|
|
 |
| | Aim Higher Maths Offered Themes |
|
Rationale
The intention of the Aim Higher Project for Maths is that it should lead students to appreciate the power, elegance and applications of the subject to everyday life. By exploring new mathematical concepts and developing familiar techniques set in unfamiliar territory, we have an expectation that students will engage and enjoy Maths even more than they do at present. The motto of the group will be “Aim Higher and you will succeed”.
We anticipate that once students have been introduced to the basic principles underpinning these topics, they will follow up their lines of enquiry and become active independent learners as a result. We are hopeful that the students in the group will gain an enriching experience and that they will want to share their discoveries with the rest of the group.
1. Step preparation.
This is for students who want to study Maths, computing or physical sciences at Oxbridge or Imperial College. Resources are supported. Past papers and solutions available.
2. AEA preparation.
This can be regarded as an extension paper in A level Maths. The questions are more challenging than the ordinary P1, 2, 3 + applied papers. No additional knowledge is required to sit this paper, however. Past papers and solutions are available.
3. Maths videos to view and discuss from the London Maths Society.
Some of these videos have follow up material, others do not. Most last about an hour.
| Pure-aholics |
Mechan-oholics |
Statist-oholics |
Computer-oholics/ Decision |
| Tangent circles |
Floating, spinning |
Marrying, voting and choosing |
Codes |
| Fractals |
Simulating the world |
A spoonful of Maths helps the medicine go down |
Big Money Maths |
| Geometry |
Maths + electric guitar |
|
|
| Music of the primes |
|
|
|
4. Programming developments in decision Maths
Student(s) are required to use Visual Basic Programming to develop programs written from the Decision Maths D1 module. D2 algorithms have not yet been written. Computer students may find this project interesting.
5. Reduction to linear form (Late Apr 05 onwards)
This is a very useful theme for science students. It enables them to find formulas from numerical data. Often involves logarithms.
6. Permutations, combinations and the game of Hex.
Useful for statisticians or pure Maths people. We can ask questions such as “In how many ways is it possible to rearrange the word Mathematics so that no 2 vowels appear next to each other. Of more practical benefit, is the problem of arranging guests round a dinner table so that George Bush is not sat next to Tony Blair.
7. Regression and more of the theory behind polynomial regression.
This theme takes a snapshot from a Pure Maths perspective. How can we generate the best fit quadratic or degree 3 curve to a given set of data. Extensions are possible for statisticians, with reference to modules S4,5,6.
8. Interview practice: Maths questions.
This will provide useful support for any student who might get asked Maths questions at interview. It is a must if you are applying to Oxbridge.
12. Problem solving skills working through puzzle book.
Dave and Andrew have plenty of brain teasers to keep you up all night. If you are one of those kinds of people that can’t say no, then opt for this.
13. Preparation for Maths challenge and Huddersfield contest.
Every year we run the Maths challenge in college. This is part of a nationwide competition. It takes place in November. You get a certificate if you do well and may get through to the next round. If you haven’t volunteered, your name will be down on the sheet anyway. The Huddersfield contest is a chance to pit your wits against colleges in nearby towns. Greenhead College thinks they are the best. Let’s teach them a lesson.
14. University trips and Aim Higher visits.
If all goes well, we would like to organise a trip somewhere. Newton has said we can come round to his place if we are prepared to travel that far. See where the apple fell.
Maybe we could visit the met office or Health service (stats).
16. Fractals.
This option would be of interest to Pure Maths people and computer scientists. Some might say Modern Art, we might say 
17. The Maths of Sport (towards the end of the course?)
A course of interest for mechanics/physics students involving spin, bounce, air resistance and physical phenomena. It would be based on “The physics of ball games” which is an excellent book.
18. Aspects of group theory.
This is an interesting introduction to basic group concepts. Abstract algebra will be new to all students at college. It would be useful for students taking a Maths degree.
20. Decision Maths with Lindo
Introduction to the Lindo software, modeling D1 and D2 material as LP problems and then using Lindo and interpreting the results. Useful for Computer science and Dec Maths.
21. Calculus of small increments (Late April 05 onwards)
A nice little topic that is very useful in science. When one variable changes by an amount, we might need to investigate the changes to another variable.
22. Island problem
A heuristic problem for computer scientists. Given an island, not necessarily convex. How can you find the furthest point from the sea? Answers on a postcard please.
23. Sigma converted to integral (May 05 onwards)
A study of the Euler Maclaurin summation formula. There are links for stats people, and Pure people could become interested in this.
25. Forming serious relationships with polynomials
This is a Pure Maths area looking at the relationships between the sums and products of polynomials. It is possible to transform the roots of a polynomial, without knowing the actual roots.
26. Studying difference equations
This is the discrete version of differential equations. You will have met recurrence relations like  but how can we find the 100 th term without caring about the 99 before it ?
Useful in mortgage calculations, modeling population growth, Dec Maths.
28. Dissecting a circle
Follow the pattern: 2, 4, 8, 16, ?? No it’s not 32 ! Useful for Pure maths. Involves proof.
29. 101 Proofs of Pythagoras
An open-ended investigation to solving Maths’ most famous theorem.
30. Euler’s formula for the platonic solids
Pure Maths proof techniques are used to explain this fascinating formula. Dec Maths.
31. Magic Squares
How to construct a magic square. This will be of recreational interest to any student.
32. A multitude of linear equations: direct and iterative methods
Pure maths and computing students will find this interesting. General methods given.
33. Modelling using dimensional analysis
This will be of interest to Physics students. It will involve the algebra of dimensions.
34. Queues on the M5
A must for modelers who are interested in solving applied Maths problems. Random numbers will be used to simulate arrivals. Software is available. Extension activities available for stats and computing students.
35. Ride on the octopus at Alton Towers.
It should be clear to the naked eye that DHG thought this one up. A definitive look at loci and curve stitching. Could be useful in mechanics and will possibly involve Autograph.
36. Geometry from basics
A complete understanding of geometry starting from a dot. Good for pure Maths.
39. Sphere of Influence
Statistical methods to solve decision maths problems. Useful in business.
41. Code breaking and the Euclidean Algorithm.
This option is a bit sketchy for Pure Maths. Could involve modular arithmetic perhaps.
Probably will involve strange things called continued fractions.
42.Series for and e
This could involve a competition to find the fastest convergent series. On your marks, get set, iterate !
43. Differentiation from first principles (Late Apr 05)
This will involve a complete understanding of the formulas behind 
44. ISBN Coding
This option will investigate Bar codes on everyday products we buy at the supermarket and making sense of the Maths behind these codes. Useful for computer scientists and Pure Maths.
45. Bin packing in two dimensions
This option will extend the ideas from the problem studied in Decision Maths Module D1.
46. Partitions
This is an exercise in Pure Number theory. You will be encouraged to do some research and present your findings based on, for example, how many ways are there of adding coins of different denominations together to make a pound coin.
47. The Gravity model in Geography
This will appeal to students interested in social science, physics, and Business Studies. If you like going shopping you will find this an interesting option.
48. Pecking order and Doodles
Strangely enough, there is Maths even in doodles and when hens lay eggs. Think of this option as an investigation full of surprises, or just good fun.
49. Maths of Stock control
This will be useful for people interested in Business applications of Mathematics.
50. Archimedes and Pi
A geometrical investigation in the hunt to find an accurate value to pi.
51. Jenga overload
For mechanics boffs, who want to study overhanging bricks. A hard hat will need to be worn for this.
52. Towers of Hanoi
How did the Ancient Egyptians move stones? Find out by selecting this option. Recursion theory may be introduced.
53. Icing on the mathematical cake
For those of you with culinary skills, this option enables you to combine your Maths with a taste for desert. The option will use differentiation in its sweetest form.
54. Driving safely on newly surfaced roads
An investigation into those formulas used in the construction of the highway code. Who needs speed cameras when trigonometry and inequalities will do the trick. |
|
|
|
|
| |
|
|
|
