Module MATH1012: CORE MATHEMATICS A

Department: MATHEMATICAL SCIENCES

MATH1012: CORE MATHEMATICS A

Prerequisites

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

Corequisites

• None.

Excluded Combination of Modules

• Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) and Foundation Mathematics (MATH1641) may not be taken with or after this module.

Aims

• This module is designed to follow on from, and reinforce, A level mathematics.
• It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
• There will be opportunities to gain experience with the Maple computer package.
• Aim: to give a utilitarian treatment of some important mathematical techniques.
• Aim: to develop geometric awareness and familiarity with vector methods.

Content

• A range of topics is treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
• A rigorous approach is expected.
• Elementary functions of a real variable.
• Limits, continuity, differentiation and integration.
• Ordinary Differential Equations.
• Partial Differential Equations.
• Fourier series.
• Geometry in 2 and 3 dimensions.
• Vectors, lines, planes, eigenvalues.
• Complex numbers.
• De Moivre's theorem, roots of unity.
• Geometry in R3 with examples from Mechanics.
• Multiple Integration.
• Taylor's theorem.
• An Introduction to Probability.
• Discrete and continuous probability distributions.
• Surfaces in three dimensions.
• Matrix Algebra in 2 and 3 dimensions.
• Algebra: Prime numbers, divisors, modular arithmetic.
• Permutations.
• Elementary group theory.

Learning Outcomes

• By the end of the module students will: be able to solve a range of predictable or less predictable problems in Calculus, Geometry, Algebra and Probability.
• have an awareness of the basic concepts of theoretical mathematics in the fields of Calculus, Geometry, Algebra and Probability.
• have a broad knowledge and basic understanding of these subjects demonstrated through one of the following topic areas: Calculus: Limits, continuity, differentiation, integration.
• Ordinary Differential Equations.
• Partial Differential Equations.
• Taylor's Theorem.
• Geometry: Vectors, lines and graphs of functions in the plane.
• Complex numbers.
• Vectors, lines and planes in 3-space.
• Matrix Algebra.
• Algebra: Factorisation of integers and common divisors.
• Arithmetic modulo n.
• Permutations.
• Elementary group theory.
• Probability: Conditional probability, Bayes Theorem and independence.
• Discrete random variables and distributions.
• Expected value, variance and the weak law of large numbers.
• Continuous random variables, particularly the Normal.
• The Central Limit Theorem.

• Students will have basic mathematical skills in the following areas: Modelling, Spatial awareness, Abstract reasoning, Numeracy.

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.
• 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.
• Experience with the Maple computer package reinforces the ability to succeed in routine elementary calculation and to enable students to recognise their own computational errors.
• The examination provides a final assessment of the achievement of the student.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

- Two written assignments weekly during the first 2 terms. Normally, each will consist of solving problems and will typically be one to two pages long. Students will have about one week to complete each assignment. - 45 minute collection paper in the first week 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