Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Faculty Handbook 2019-2020

Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

Department: Mathematical Sciences

MATH1597: Probability I

Type Open Level 1 Credits 10 Availability Available in 2019/20 Module Cap None. Location Durham

Prerequisites

  • Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

Corequisites

  • Calculus I (MATH1061)

Excluded Combination of Modules

  • Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

Aims

  • This module will give an introduction to the mathematics of probability.
  • It will present a mathematical subject of key importance to the real-world ("applied") that is nevertheless based on rigorous mathematical foundations ("pure").
  • It will present students with a wide range of mathematical ideas in preparation for more demanding and specialized material later.

Content

  • A range of topics are treated each at an elementary level to give a foundation of basic concepts, results, and computational techniques.
  • A rigorous approach is expected.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will:
  • be able to solve a range of both routine and more challenging problems in probability theory.
  • be familiar with the basic mathematical concepts of probability theory.
  • have a broad knowledge of the subject area demonstrated by detailed familiarity with the following topics:
  • set theoretic framework for sample spaces and events, including notions of countable and uncountable sets;
  • event calculus, probability axioms, conditional probability, Bayes's formula, independence of events;
  • discrete and continuous random variables and their distributions, including particular familiarity with the binomial, Poisson, normal and exponential distributions;
  • joint distributions, conditional distributions, and independence of random variables;
  • expected value of a random variable, variance, covariance, and moment generating functions;
  • tail inequalities, the weak law of large numbers, and the central limit theorem.
Subject-specific Skills:
  • Students will have basic mathematical skills in the following areas: modelling, abstract reasoning, numeracy
Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
  • Tutorials provide active engagement and feedback to the learning process.
  • Students are expected to develop their knowledge and skills with at least 50 hours of self-study.
  • Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
  • Initial diagnostic testing and associated supplementary problems classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.
  • The examination provides a final assessment of the achievement of the student.

Teaching Methods and Contact Hours

Activity Number Frequency Duration Total/Hours
Lectures 27 3 pw in wks 1-3, 5, 7, 9; 2 pw in wks 4, 6, 8, 10; 1 revision in wk 21 1 Hour 27
Tutorials 5 1 pw in wks 3, 5, 7, 9; 1 revision in wk 21 1 Hour 5
Problems Classes 4 1 pw in wks 4, 6, 8, 10 1 Hour 4
Support classes 9 1 pw in wks 2-10 1 Hour 9
Preparation and Reading 55
Total 100

Summative Assessment

Component: Probability Examination Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
Written examination 2 hours 100% Yes

Formative Assessment:

Weekly written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students. Students will have about one week to complete each assignment. Students will have about one week to complete each assignment. A 45-minute Collection paper at the beginning of Epiphany term.


Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University



If you have a query about a specific module or degree programme, please contact the appropriate department.

If you have a question about Durham's modular degree programmes, please visit our FAQ webpage.  If you have a question about modular programmes that is not covered by the FAQ, or a query about the on-line Faculty Handbook, please contact us using the Comments and Questions form below.