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Mathematics 1ES (MATH 10500)

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Administrative Information

  1. Unit number and title: MATH 10500 Mathematics 1ES
  2. Level: C/4 (Open)
  3. Credit point value: 40 credit points
  4. Year: 12/13
  5. First Given in this form: 1992/93 in its present form, under the name Mathematics 1E
  6. Unit Organiser: Isaac Chenchiah
  7. Lecturer: Dr. Isaac Chenchiah, Carl Dettmann, Dr. Li Chen
  8. Teaching block: 1 and 2
  9. Prerequisites: GCSE grade C or better.

Unit aims

To revise elementary mathematics in GCSE (bearing in mind the needs of students who have not studied mathematics for 2 years or more). To introduce basic algebra, trigonometry, calculus and statistics as useful tools for science students.

General Description of the Unit

The unit develops algebra and elementary calculus roughly from GCSE to A level standard, bearing in mind the needs of students of the sciences. The last section of the unit provides a short introduction to the aspects of statistics of most interest and importance to scientists, covering 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 without A level mathematics: Mathematics 1EM. It is identical to this unit for the first 17 weeks. From week 18 onwards, Mathematics 1EM has more mathematics while Mathematics 1ES has statistics (and a few lectures on mathematics).

The statistics element of this unit is available as a stand-alone 10cp unit, Elementary Statistics.

Teaching Methods

3 lectures per week, with weekly tutorials in weeks 1 - 18. Marked work is returned to the students and difficulties explained in the tutorials. To assist students in evaluating their progress, short tests are held in weeks 5 and 9. In the last six weeks, on statistics, there are practical assignments and computing lab classes.

Learning Objectives

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

  • perform basic algebraic manipulations
  • sum arithmetic and geometric series
  • solve linear, simultaneous linear, and quadratic equations
  • use numerical methods to find areas under curves, etc.
  • use trigonometry and vectors
  • differentiate and integrate simple functions and know the physical meaning of the derivative and integral.
  • 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 allowed to continue in your degree programme. You should consult your Faculty Handbook or your departmental information.

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

  • 10% from the midsessional examination in January.
  • 65% from written examinations in May/June (details below).
  • 25% from four practical Statistics assignments.

To assist students in evaluating their progress, short tests are held in weeks 5 and 9.

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.

Summer Examination

Candidates in Maths 1ES examinations may use calculators.  Only calculators of 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 2 papers on algebra and calculus. There is no examination in statistics, which is assessed by coursework.

  • Paper 1 lasts three hours. Section A has 10 short questions, all of which should be answered; it carries 40% of the marks for this paper. Section B  has 6 longer questions,of which you should do FOUR. If you do more than four, your best four answers will be used for assessment. Section B carries 60% of the marks for this paper. Paper 1 examines material from E1.
  • Paper 2 lasts 1½-hours. Section A has 5 short questions, all of which should be answered; it carries 40% of the marks for this paper. Section B has three longer questions of which you should do TWO. If you do more than two, your best two answers will be used for assessment. Section B carries 60% of the marks for this paper. Paper 2 examines material from E2.
  • Paper 1 contributes 40% to your overall mark for the unit; paper 2 contributes 25% to your overall mark for the unit.

January examinations

The Mid-sessional January Progress Examinations are right at the start of the second term. This term begins on Friday 11th January 2013, and the examination for this unit may be on Friday 11th January or Saturday 12th January. IT IS YOUR RESPONSIBILITY to ensure that you are in Bristol to sit the examination; otherwise your mark will be zero (unless you have a certified illness or other special circumstances of which the school has been notified). You will be notified of the date, time and place of the January examination before the end of the first term.

These examinations are compulsory: you must attend. Your mark in the January examination for the unit will contribute 10% to the final assessment mark for the unit in June. It should also give you, and us, an indication of how well you are coping with the unit.

 The January 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 this paper. Section B  has 3 longer questions,of which you should do TWO. If you do more than two, your best two answers will be used for assessment. Section B carries 60% of the marks for this paper. Candidates may use calculators. Only calculators of 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.

September Examinations

If you fail Mathematics 1ES in June, you may (depending on which Faculty you are in and how you have done in your other units) be allowed to resit it in September. The September examination papers have the same structure as in June, and there will also be a practical assessment in Statistics.

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 must attend the January examination,
  • 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

Mant textbooks cover the mathematics taught in this unit, for example:

  • 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

Numbers in brackets refer to weeks.


I Algebra & Differential Calculus: 36 Lectures
 
(1&2) Algebra: Terminology and priorities of operations; Function notation and evaluation; Laws of indices; Gathering like terms; Expansions; Factorisation; Linear equations; Linear inequalities; Changing the subject of formulae; Equation of straight line; Algebraic fractions; Factorisation & solution of quadratics; Factorising polynomials.
 
(3&4) Calculus: Gradient of curve as limit of chord; Derivatives of powers of x and polynomials; Tangents and Normals; Chain Rule; Product and Quotient Rules; Stationary points; Second derivative and testing for max/min/point of inflexion; Optimisation problems.
 
(5&6) Growth functions, exponentials & logarithms: Exponential growth and decay; Logarithms; Derivatives of exponential and logarithmic functions; Compound interest
 
(7) Sequences & Series: Generating sequences by formulae or inductive rules; Arithmetic Progressions; Geometric Progressions; Applications.
 
(8) Circles and pairs of straight lines: Circles: Equations; Finding centre and radius from equation; Whether lines cut or miss, whether points lie inside or outside; Simultaneous linear equations, including cases with no/many solutions.
 
(9-11) Trigonometric Functions: Definition of sin, cos and tan; Graphs; Inverses; Simple trignometric equations; Arc length & sector area; Limit of (sin x)/x; Sine and Cosine rules; Differentiation of trigonometric functions; Implicit differentiation.
 
(12) Complex Numbers: Definition in the form a + ib; r (cos A + i sin A); multiplication; the Argand diagram
 
II Integral Calculus & Vectors: 15 lectures
 
(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).Vector equations of lines and planes. Vector perpendicular to two given vectors.
 

III Basic Statistics: 18 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

Maths 1ES is intended to teach you something useful that you will use in your honours subjects. You must take it seriously and not just concentrate on your honours subject. A third of your time 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 allowed to continue studying your Honours subject unless you obtain 40 credit points from this course; see the Award of Credit Points section for more details.

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 weekly during the first 18 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.

There are 3 lectures each week as well as the tutorials. In the last 6 weeks there will be compulsory practical sessions for the Statistics component of the unit, using Microsoft Excel to display and analyse data. The practical exercises will be marked and will count: see the Assessment section below. No previous knowledge of computing is assumed. The times of the practical sessions for each student will be assigned early in the year.

In weeks 5 and 9 there will be short tests. 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.