Algebra

Code

MATH1104

School

Mathematical Sciences

Level

1

Credits

20

Semesters

Full Year UK

Summary

This is a year-long module that introduces students to basic concepts of algebra and aims to provide students with familiarity with both reading and writing in the language of formal mathematics. Topics include:
· Introductory number theory.
· Modular arithmetic.
· Equivalence relations.   
· Permutations.
· Group theory (with many examples and including study of subgroups, homomorphisms and the order of groups).
· Introduction to the algebra of polynomials.

Target Students

Single Honours and Joint Honours students from the School of Mathematical Sciences.

Co-requisites

Modules you must take in the same academic year, or have taken in a previous year, to enrol in this module:

• Core Mathematics (MATH1101)

Classes

• Twenty-two 1-hour workshops each week for 3 weeks

Teaching will be through a variety of methods, ranging from traditional lectures and computing sessions through flipped learning, with the delivery tailored to the material on a week-by-week basis.

Assessment

• 40% Coursework 1: Summative assessment based on tasks distributed through the year.
• 40% Exam 1 (2-hour): Written examination. Assessed at the end of the Spring semester.
• 20% Exam 2 (1-hour): Class test

Assessed by end of spring semester

Educational Aims

Learning Outcomes

A student who completes this course successfully will be able to:

L1 - Appreciate the essential role within mathematics played by formal definitions and precise, rigorous arguments, and that abstraction leads to both generalisation and simplification of concepts;

L2 - State and apply the standard definitions of, and results concerning, basic concepts of set theory and number theory (such as partitions, equivalence relations, and prime factorization) that underpin modern applications;

L3 - Solve simple problems involving integers, rational numbers and irrational numbers, using concepts from elementary number theory (such as prime numbers, divisibility of integers, the fundamental theorem of arithmetic, and modular arithmetic);

L4 - Prove or disprove basic algebraic statements by building logical arguments and proofs, clearly and precisely expressed using standard mathematical notation;

L5 - State and prove simple results about groups, both for general abstract groups and for concrete examples;

L6 - Carry out calculations (including products and inverses) in a range of standard groups (for example permutation groups, dihedral groups, groups of integers modulo n) and calculations related to the algebraic theory of polynomials.

Conveners

• Dr Daniel Nicks