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Mathematics 1FS (MATH 10530)

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Contents of this document:

Administrative Information

  1. Unit number and title: MATH 10530 Mathematics 1FS
  2. Level: C/4 (Open)
  3. Credit point value: 20 credit points
  4. Year: 12/13
  5. First Given in this form: 2008/2009
  6. Unit Organiser: Carl Dettmann
  7. Lecturer: Dr Carl Dettmann and Dr Li Chen
  8. Teaching block: 2
  9. Prerequisites: Equivalent to GCSE grade C plus International Foundation Programme diagnostic test

Unit aims

To introduce integral calculus, vectors and elementary statistics as useful tools.  This unit is primarily for International Foundation Programme students seeking further study in science or other numerate subjects.

General Description of the Unit

The unit introduces integration and vectors as well as providing a short introduction to the aspects of statistics of  most interest and importance to scientists. It will cover the basics of probability, statistical distributions, hypothesis testing, regression etc. No previous statistical knowledge will be assumed.

Relation to Other Units

There is another unit for students taking the Foundation Year programme: Mathematics 1FM. It is identical to this unit for the first 5 weeks. From week 18 onwards, Mathematics 1FM has more mathematics while Mathematics 1FS has statistics.

 

Teaching Methods

3 lectures per week, with weekly tutorials week in weeks 13 - 18. Marked work is returned to the students and difficulties explained in the tutorials. In the last six weeks, on statistics, there are practical assignments and computing lab classes.

The MAPLE software is used in the algebra and calculus part of the course, and EXCEL is used for statistics practical sessions.

Learning Objectives

At the end of the unit students should be able to:

  • use numerical methods to find areas under curves, etc.
  • integrate simple functions and know the physical meaning of the integral.
  • use vectors 
  • have an insight into the value, use and interest of statistical methods in scientific work and thought
  • apply simple statistical methods in their own scientific work, and to understand what they are doing
  • understand the statistical jargon used in scientific papers.

Assessment Methods

You should realise that if you fail the unit, or fail to gain the credit points, the consequences may be very serious. You may not be granted a certificate.

To pass the unit your final assessment mark must be 40 or over. This assessment mark will be made up as follows:

  • 50% from written examinations in May/June (details below).
  • 50% from four practical Statistics assignments.

In addition weekly work will be marked.

Assessment of Statistics

Each week's assignment is to be handed in at the end of the lecture on the date specified when the assignment is set.

The statistics assessment as follows:

Assignment 1 gives 20% of the Statistics mark.
Assignment 2 gives 25% of the Statistics mark.
Assignment 3 gives 25% of the Statistics mark.
Assignment 4 gives 30% of the Statistics mark.

Assignments handed in late will receive reduced or no marks.

There may be good reasons, such as illness, for handing in work late or not attending the required practical classes: you must provide evidence, such as a doctor's note, in order for marks to be awarded in such cases.

Details of the Summer Examination

Calculators of an approved type (non-programmable, no text facility) are allowed. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination
room.

The final examination in May/June consists of one paper on algebra and calculus. There is no examination in statistics, which is assessed by coursework.

  • The examination paper lasts one-and-a-half-hours. Section A has 5 short questions, all of which should be answered; it carries 40% of the marks for the paper. Section B  has three longer questions, of which you should do TWO; if you do more than two, your best two answers from this section will be used for assessment Section B carries 60% of the marks for this paper.
  • The examination paper has questions on E2. and contributes 50% to your overall mark.

September Examinations

If you fail Mathematics 1FS in June, you may (depending on which programme you are on and how you have done in your other units) be allowed to resit it in September. The September examination paper has the same structure as in May/June.  There is also a practical assessment for the statistics component.

 

Award of Credit Points

To be awarded the credit points for this unit you must normally pass the unit, i.e. you must achieve an assessment mark of 40 or more.

The assessment mark is calculated as described in the Assessment section above. Details of the university's common criteria for the award of credit points are set out in the Regulations and Code of Practice for Taught Programmes at http://www.bristol.ac.uk/esu/assessment/codeonline.html

In particular, for this unit:

  • students must attend the compulsory computer practicals during the statistics part of the course, otherwise they may be barred from the final examination and hence fail the unit without credit points,
  • students are expected to attend all the relevant tutorials,
  • students are expected to hand in attempts every week to the weekly exercises set.

Note: we will make allowances for illness and other such good reasons, PROVIDED that you follow the School of Mathematics procedures: you must inform the Undergraduate Student Administrators in Mathematics and submit a completed Extenuating Circumstances form (available from the School) together with supporting written documentation (e.g. a doctor's certificate, specifying the date(s) you were unable to undertake academic work).

Transferable Skills

  • Increased skills in handling mathematics and data of all kinds (numeracy skills).
  • Use of EXCEL for simple statistical work

Texts

Recommended (but not required textbook):

  • Understanding Pure Mathematics, A.J. Sadler and D.W.S. Thorning (Oxford University Press 1995)

You may also find the following books helpful:

  • Help yourself to algebra, Hugh Neill (Longman 1996)
  • Mind the Gap, bridging the gap between GCSE and AS Maths, Roger Cahalin, Alessandra Desbottes & Suzanne Doyle (Coordination Group Publications 2002

Recommended (but not required) for statistics:

  • Gerald Keller, Applied Statistics with Microsoft Excel, published by Duxbury.

You might also find this useful: Bruce E. Trumbo, Learning Statistics with Real Data, Duxbury

Syllabus

E2 Vectors & Calculus: 15 Lectures

Numbers in brackets refer to weeks.

(13) Areas by Summation: Mid-ordinate rule, Trapezium rule, Area under curve, Fundamental Theorem of Calculus

(14) Integration: Integration of polynomials; Definite & indefinite integrals.

(15-17) Vectors: Definition of vector; Notation; Addition; Multiplication by scalar; Scalar product; Distributive rule; Use of i, j, k; Angle between vectors in 2-D & 3-D; Proof of Pythagoras; Formula for cos(A+B) only. Vector equations of lines and planes. Vector perpendicular to two given vectors.


Basic Statistics: 17 Lectures
Probability:

The use of probability in everyday life and in scientific modelling.
Exploratory methods: plotting data, structure exposed by suitable plots, log-log plots, outliers.

Probability models:

Use of probability to model observed phenomena.
Discrete variables: The Binomial distribution, the Poisson distribution
Continuous variables: The Normal distribution: its uses and misuses.

Inference:

Hypothesis testing and confidence intervals:
What is a p-value? One- and two-sided tests. Standard errors.
One and two sample t-tests, One-way Analysis of Variance.

Regression:

Dependence and independence. Linear regression and correlation. Percentage of variability explained.

Advice for Students

Advice for Students

Maths 1FS is intended to teach you something useful that you will use in your subsequent honours studies. You must take it seriously and not just concentrate on your language studies. A third of your time in teaching block 2 should be spent on mathematics, and bear in mind that this time includes practical sessions in your other subjects. (Working at mathematical problems is similar to working in the laboratory.) You will not be qualify for the certificate unless you obtain 20 credit points from this course; see the Award of Credit Points section for more details.

The topics covered are closely related to the A level syllabus, and the first required book is an A level text; see the Texts section below. If at a future date you need to go further into mathematics, then you can get other books, or look in the library for similar texts containing many worked examples. In addition, you will probably need to practise your basic algebraic manipulative skills. For this it is recommended that you purchase and work through exercises in the book Help yourself to algebra by Hugh Neill.

Practice is essential if you are to become competent in basic skills. Problems will be set each week, which you must hand in. You are not discouraged from working together (problems that have been worrying you for days can often be solved very quickly in discussion with your friends). But you must hand in your own write-up, even if it is based on ideas that may have been discussed with other people. Handing in identical pieces of work is not acceptable.

Tutorials in groups of about 12 to 15 students will be held weekly week during the first 6 weeks. You are expected to attend and talk about the material being covered. Problems not set to be handed in can be attempted during the tutorial, and any other problems raised. In the first week the tutorial time will be used to introduce you to the MAPLE software (see below).

There are 3 lectures each week as well as the tutorials.  If in doubt, ASK - that is what lecturers and tutors are for; don't assume everyone else knows what is going on - if you don't understand something, other people probably don't either, and will appreciate your asking about it.

In weeks 5 and 9 there will be short tests on Algebra. You will take the tests during the tutorial period. Completion of these tests may be required for the award of credit points.

If you find that you still have problems unsolved at any time, please ask for extra help.

Calculators

Don't feel that you have to buy a graphics calculator - they are not essential, and graphic calculators may not be used in the examination. An ordinary scientific calculator (cost £5 to £10) is sufficient, but you should check that it satisfies our requirements on calculators used in examinations:

  • no graphics capability
  • no complex number or matrix or symbolic algebra or calculus capability
  • no equation-solving capability
  • no capacity to store text
  • no programming capability.