The Use of Mathematics in Post-16 Mathematics A-Level Course

1. Post 16 Mathematics A Level Course

2. What is the use of Mathematics? The use of arithmetic, and the display of information by means of graphs are an everyday occurrence. Here are a few examples of the use of mathematics:

3. What is the use of Mathematics? • Geography and Environmental Sciences - Maps, Topology, Weather prediction • Silicon Chips - Complex Number theory • Computer Disks - Fractal theory • CD players and computing - error correcting codes • Supercomputers - applying speed and accuracy • Physical sciences (Physics, Chemistry, Oceanography, Astronomy, Ecology, Biology & Medicine) - Development of theories, laws of population change, analysis of data, causes of illness and utility of new drugs. • Airplanes - Airflow and control systems • Body Scanners - Construction of images from a number of X - ray images

4. What is the use of Mathematics? • Quantum Physics and DNA structures - Knot theory • Oil Recovery • Engineering • Artificial Intelligence • Molecular modelling and general materials • Economics and Finance • Business modelling • Signal Processing • Industry Maintenance • Sales, Marketing and Buying • Operational Management • Electrical Engineering and Electromagnetics • Buildings and general structures

5. 422 University Courses Mathematics is offered as a Single subject, as part of a Joint degree, or as a vital part of courses at Degree level 422 in Great Britain alone.

6. University Maths Courses • Calculus and Analysis • Modelling with differential equations • Linear Algebra • Modelling force of motion • Discrete systems • Multiple integrals • Vector calculus • Real and Complex analysis • Stochastic processes • Fourier Series • Dynamical systems • Rotational Dynamics • Environmental Statistics • Fluid Mechanics • Quantum Mechanics • Set Theory • Special Relativity

7. Careers All of the jobs shown either: • Require the relevant qualification or • Need topics covered at the level of the qualification

8. Accountant: Industry and Commerce Accountant: Private Practice Accountant: Public Service Accounting Technician Actuary Air Traffic Control Officer Arboriculturist Archaeologist Architect Architectural Technician Army Officer Auditor Bailiff Bank Manager Bank Officer/Cashier Biochemist/Biochemistry Technician Biologist/Biology Technician Building Control Officer Building Services Engineer/Technician Building Society Clerk Building Society Manager Building Technician Bursar Buyer/Purchasing Officer Careers

9. Cabinet-maker Cameraman/woman (TV/Film) Catering/Restaurant Manager Chartered Engineer Chartered Engineer (Chemical) Chartered Engineer (Mechanical) Chemist/Chemistry Technician Civil Service Executive Officer Commodity Broker Computer Applications Programmer Computer Operator Computer Service Engineer/Technician Computer Systems Analyst Computer Systems Programmer / Software Engineer Conference Manager/Organiser Construction Manager Construction Planner Countryside/Conservation Officer Designer: 3-Dimensional (Craft) Designer: 3-Dimensional (Product) Designer: Graphic Designer: Textile Distribution Manager Draughtsman/woman (Engineering) Economic Development Officer Economist/Economics Advisor Editor: Publishing Engineer - Design Engineer - Manufacturing Careers

10. Engineer - Research and Development Engineer: Chartered Civil/Structural Engineer: Incorporated/Technician - Civil Engineer: Incorporated/Technician – Electrical Engineer: Incorporated/Technician - Electronics Entertainment Manager Environmental Health Officer Estate Agent/General Practice Surveyor Estates Officer - Public Sector Forensic Scientist Forest Officer/Manager Freight Forwarder Geologist/Geological Technician Health Service Manager HM Customs and Excise Officer HM Inspector of Taxes/Revenue Executive Hotel Manager Incorporated Engineer/Technician Incorporated Engineer/Technician (Chemical) Incorporated Engineer/Technician (Mechanical) Insurance Broker Insurance Claims Official Insurance Loss Adjuster Insurance Salesperson Insurance Surveyor Insurance Underwriter Laboratory Technician Leather Technologist Lecturer: Further/Tertiary education Lecturer: Higher Education Careers

11. Legal Executive Leisure Centre Manager Local Government Administrator Local Government Revenue Officer Marketing Manager Materials Technologist Medical Physics Technician Merchandiser Merchant Navy Deck Officer Merchant Navy Engineering Officer Meteorologist Microbiologist/Microbiology Technician Money Advisor Oceanographer Operational Research Scientist Optician: Opthalmic/Optometrist Pensions Manager Pharmacist Photographic Technician Physicist/Physics Technician Physiological Measurement Technician Pilot: Airline Pilot: Helicopter Printing Administrator/Technologist Production Assistant/Co-ordinator (Media/Stage) Psychologist Radiographer Royal Air Force Airman/woman Careers

12. Royal Air Force Officer Royal Marines Officer Royal Navy Officer Royal Navy Rating Sales Manager Sales Representative Scientist Secretary Stock Exchange Investment Analyst Stock Exchange Market Maker Stock Exchange Stockbroker Store Manager Surveying Technician: General Practice Surveying Technician: Quantity/Building Surveyor/Surveying Technician: Mineral/Mining Surveyor: Building Surveyor: Land/Hydrographic Surveyor: Planning and Development Surveyor: Quantity Surveyor: Rural Practice/Land Agent Surveyor: Valuation/Auctioneer Teacher: School (England & Wales) Teacher: School (Scotland) Teacher: Special Educational Needs Technician: Education Textile Dyeing Technician Textile Technician Town Planner Trading Standards Officer Transport Manager: Road Travel Agency Manager Warehouse Manager Work Study/Organisation and Methods Officer Careers

13. CHALLENGE Can you think of a job that NEVER needs Mathematics? If you can, let us know!!

14. Interesting Statistical Fact • Two people with identical A level grades – one with A Level Maths, one without! • The person with A Level Maths earns on average 10% more than the person without!!

15. What is involved? AS GCE Mathematics (3890) • Either C1, C2, and S1 • Or C1, C2 and M1 AS GCE Further Mathematics (3891) • Either FP1, D1 and S1 • Or FP1, D1 and M1

16. What is involved? Advanced GCE Mathematics (7890) Either • C1, C2 • M1 + C3, C4 + M2 Or • C1, C2 • S1 + C3, C4 + S2 + C3, C4 + S1 Or • C1, C2 • M1

17. What is involved? Advanced GCE Mathematics (7890) Advanced Subsidiary GCE Further Mathematics (3892) • C1, C2 • M1 • S1 • D1 • FP1 + C3, C4 Either + M2 Or + S2

18. What is involved? Advanced GCE Mathematics (7840) + Advanced GCE Further Mathematics • C1, C2 • M1 • S1 • D1 • FP1 + C3, C4 + M2 + S2 +FP2 Either M3 Or S3 Or D2 Or FP3 +

19. Pure Maths Section • Core Mathematics 1 (C1) (4721)(AS) Indices & Surds; Polynomials; Coordinate Geometry & Graphs; Differentiation. (Non calculator paper) • Core Mathematics 2 (C2) (4722)(AS)Trigonometry; Sequences and series; Algebra; Integration. • Core Mathematics 3 (C3) (4723)(A2)Algebra and Functions; Trigonometry; Differentiation and Integration; Numerical Methods. • Core Mathematics 4 (C4) (4724) (A2) Algebra and Graphs; Differentiation and Integration; Differential Equations; Vectors.

20. Pure Maths Section • Further Pure Mathematics 1 (FP1) (4725)(AS)Summation of series; Mathematical Induction; Roots of Polynomial Equations; Complex Numbers. • Further Pure Mathematics 2 (FP2) (4726)(A2)Rational Functions and Graphs; Polar coordinates; Hyperbolic functions; Differentiation and Integration; Numerical Methods. • Further Pure Mathematics 3 (FP3) (4727)(A2)Differential Equations; Vectors; Complex Numbers; Groups.

21. Mechanics Section • Mechanics 1 (M1) (4728)(AS)Force as a vector; Equilibrium of a particle; Kinematics of motion in a straight line; Newton’s laws of motion; Linear momentum. • Mechanics 2 (M2) (4729)(A2)Centre of mass; Equilibrium of a rigid body; Motion of a projectile; Uniform motion in a circle; Coefficient of restitution and impulse; Energy, work and Power. • Mechanics 3 (M3) (4730)(A2)Equilibrium of rigid bodies in contact; Elastic strings and springs; Impulse and momentum in two dimensions; Motion in a vertical circle; Linear motion under a variable force; Simple Harmonic Motion.

22. Statistics Section • Probability and Statistics 1 (S1) (4732) (AS)Representation of data; Probability; Discrete Random Variables; Bivariate data • Probability and Statistics 2 (S2) (4733) (A2)Continuous Random Variables; The Normal Distribution; The Poisson Distribution; Sampling and Hypothesis testing. • Probability and Statistics 3 (S3) (4734) (A2)Continuous random variables; Linear combinations of random variables; Confidence intervals and the t distribution; Difference of population means and proportions; the chi squared test.

23. Discrete Maths Section • Discrete Mathematics 1 (D1) (4736) (AS)Algorithms; Graph Theory; Networks; Linear Programming. • Discrete Mathematics 2 (D2) (4737) (A2) Game theory; Flows in a network; Matching and allocation problems; Critical Path Analysis; Dynamic Programming

24. Thank you for listening…… Any Questions??