Undergraduate Programme and Module Handbook 2005-2006 (archived)

Module MATH1041: CORE MATHEMATICS B2

Department: MATHEMATICAL SCIENCES

MATH1041: CORE MATHEMATICS B2

Type	Open	Level	1	Credits	20	Availability	Available in 2005/06	Module Cap	None.	Location	Durham

Prerequisites

Normally grade A in A-Level Mathematics (or equivalent).

Corequisites

MATH 1012 (Core Mathematics A), MATH1051 (Core Mathematics B1).

Excluded Combination of Modules

Maths for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) and Foundation Mathematics (MATH1641).

Aims

To provide (a) an understanding of sets, logic and the axiomatic development of numbers.
(b) an understanding of elementary classical Newtonian dynamics.

Content

Logic and Sets Truth tables: sets and basic manipulations, De Morgan laws, Quantifiers.
Proof and counterexample, relations and equivalence relations.
Cardinality and Countability Numbers: the axiomatic development of numbers from natural numbers to the complex plane.
Mathematical Induction, primes, Fundamental Theorem of Arithmetic.
Formal proofs of divisibility properties.
Dynamics Newton's laws, frames of reference.
Mass, force, energy, momentum, angular momentum.
Sample motions: simple harmonic oscillator.
Projectiles.
Charged particle in constant electromagnetic field.
Orbits.
Waves on strings.
Wave equation for small amplitude oscillations, separation of variables.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve a range of predictable or less predictable problems in Reasoning and Dynamics.
have an awareness of the basic concepts of theoretical mathematics in the fields of Reasoning and Dynamics.
have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas: Reasoning: Logic and Sets.
Cardinality and Countability.
Numbers.
Dynamics: Newtonian Mechanics, frames of reference, Newton's laws.
Sample motions.
Two body systems.
Waves on strings.

Subject-specific Skills:

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

Key Skills:

students will have basic problem solving 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.
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.
The examination provides a final assessment of the achievement of the student.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total/Hours
Lectures	37	2 per week	1 Hour	37
Tutorials	20	Weekly	1 Hour	20
Preparation and Reading				143
Total				200

Summative Assessment

Component: Examination		Component Weighting: 100%
Element	Length / duration	Element Weighting	Resit Opportunity
three-hour written examination		100%

Formative Assessment:

- One written assignment each teaching week. Normally it will consist of solving problems from a Problem Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment. - 45 minute collection paper in 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