CSU11001 – Mathematics I

Module Learning Outcomes

On successful completion of this module, students will be able to:

1. Produce coherent, convincing mathematical arguments that are precise in terms of both technical description and computation;
2. Operate with vectors in 2 and 3 dimensions, and apply vectors to solve basic geometric problems;
3. Derive, formulate and apply solutions for linear systems using standard methods (Gaussian Elimination, Cramer’s Rule, etc);
4. Manipulate matrices algebraically and use concepts related to matrices such as invertibility, symmetry, triangularity;
5. Recognise and employ the main ideas and techniques of basic calculus;
6. Discriminate between, and calculate, a variety of integrals.

Module Content

Mathematics is of interest to computer scientists due to the fact that it is both practical and theoretical in nature. Not only does it have a myriad of applications (e.g. in wireless communications and computer graphics), it is also of intrinsic interest to theoretical computer scientists. The mathematical techniques learned as part of this module have wider applications in areas as diverse as Business (e.g. for modelling volatility and risk), Economics (e.g. for macroeconomic policy modelling) and Engineering (e.g. for structural monitoring).

These learning aims are achieved by providing students with an introduction to the mathematical techniques which lie at the foundation of many real-world applications in Computer Science, Engineering and the Social Sciences. This module aims to develop the students’ skills and abilities in the mathematical methods necessary for solving practical problems. One of the key objectives for this module is to introduce students to the learning styles needed for university level mathematics. Students will be encouraged to develop the independent, reflective learning skills needed for success at University level.

Specific topics addressed in this module include:

• Lines, planes and vectors, dot and cross product;
• Matrices and the solution of linear systems;
• Eigenvalues, Eigenvectors and their applications;
• Vector spaces, linear independence and span, bases and dimension;
• Linear operators, matrix of a linear operator with respect to a basis;
• Differentiation of functions and the use of derivatives to graph functions, solve extremal problems and related rates problems;
• Integration of functions using substitution, integration by parts, partial fractions and reduction formulae;
• Using calculus to find areas, volumes, length of curves and averages.

Teaching and Learning Methods

The module will employ a variety of teaching and learning methods including formal lectures, large group problem solving classes and small group tutorials.

Assessment Details

Students must submit a meaningful attempt at a minimum of 80% of the assignments set for this module.

Note that it may be necessary to reduce the number of assessed assignments (if insufficient demonstrators are available). The weights of these assignments will be redistributed over the other assignments in the semester.

Reassessment Details

In-person Examination. Time Limited (2 hours, 100%)

Contact Hours and Indicative Student Workload

• Elementary Linear Algebra (Applications Version), Howard Anton, Chris Rorres, Wiley.
• Calculus: Early Transcendentals, Single Variable Howard Anton, Irl Bivens, Stephen Davis, Wiley.

Module Pre-requisites

Prerequisite modules: N/A

Other/alternative non-module prerequisites: N/A

N/A

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