Mathematics Tutorial

Module Identifier: MA01000
Module Title: Mathematics Tutorial
Academic Year: 2027/2028
Semester: Semester 1 Taught over 2 semesters
Co-ordinator: Dr Alexander Pitchford
Reading List: View on Aspire
Other Staff: Mrs Rosemary Rogers; Dr Alexander Pitchford; Professor Simon Cox

Assessment

Assessment Type	Assessment details	Proportion
Semester Assessment	Coursework: Mark based on attendance at tutorials and submitted assignments	30%
Semester Exam	Written Exam: 2 Hours	70%
Supplementary Assessment	Supplementary Assessment: Blackboard Test.	30%
Supplementary Exam	Supplementary Written Exam: 2 Hours	70%

Learning Outcomes

On successful completion of this module students should be able to:

Solve polynomials of small degree; obtain and use relations between the roots and coefficients of polynomials.
Simplify algebraic expressions and inequalities.
Compute with trigonometric functions and use trigonometric identities.
Apply basic set operations; explain the difference between integers, rational and irrational numbers.
Manipulate vectors and evaluate their products. Translate between Cartesian and polar coordinates.
Represent complex numbers in different forms and apply algebraic operations to them.
Define a function and its domain and range; sketch graphs of simple functions.
Determine properties of sequences and series
Manipulate expressions involving the exponential and logarithmic functions.
Prove simple theorems about numbers.

Brief description

The module consists of a weekly two hour problem class, throughout both
semesters, at which students are required to work, individually or in groups, on
set problems. Difficulties arising in other Year 0 mathematics modules will be
discussed and resolved.

Aims

The aims of this module are to increase awareness in the technical skills
associated with basic mathematics; to develop analytical skills; to develop an
appreciation of the need for logical order and precision; to increase confidence
in understanding and solving mathematical problems.

Content

1. BASIC ALGEBRA, SETS, INEQUALITIES. Manipulation of mathematical expressions, introduction to set theory, number sets, solving inequalities.

2. SURDS, LOGARITHMS, EXPONENTIAL FUNCTION. Simplification of surds, laws of exponentials and logarithms.

3. POLYNOMIALS. Factors and roots. Completing the square, Vieta's Theorem, Factor and Remainder Theorems.

4. TRIGONOMETRY. Trigonometric functions and identities. Graphs of trigonometric functions. Trigonometric equations.

5. FUNCTIONS AND SEQUENCES. Domain, codomain, image, composition and inverse of functions. Arithmetic and geometric sequences and series.

6. COORDINATE AND VECTOR GEOMETRY. 2D and 3D vector arithmetic. Cartesian and polar coordinate systems.

7. COMPLEX NUMBERS. Complex number representations. Real and imaginary parts, modulus and argument, De Moivre's Theorem, complex roots.

8. PROOFS. Introduction to proofs in number theory.

Module skills

Skills type	Skills details
Application of Number	Required throughout the course.
Communication	Written answers to exercises must be clearand well structured.
Improving own Learning and Performance	Students are expected to develop their ownapproach to time-management regarding thecompletion of assignments on time andpreparation between classes.
Information Technology	Use of Blackboard
Personal Development and Career planning	Completion of task (assignments) to setdeadlines will aid personal development.
Problem solving	The assignments will give the studentsopportunities to show creativity in findingsolutions and develop their problem solvingskills.
Subject Specific Skills	Broadens exposure of students to topics inmathematics.

Notes

This module is at CQFW Level 3