Algebra
| Code | School | Level | Credits | Semesters |
| MATH1107 | School of Mathematical Sciences | 1 | 20 | Full year China |
- Code
- MATH1107
- School
- School of Mathematical Sciences
- Level
- 1
- Credits
- 20
- Semesters
- Full year China
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 students from the Department of Mathematical Sciences
Classes
- Three 1-hour workshops each week for 24 weeks
Assessment
- 40% Coursework 1: Summative assessment based on tasks distributed through the year.
- 20% Class Test 1 (1-hour): Written class test - Autumn
- 40% Exam 1 (2-hour): Written examination - Spring
Assessed by end of spring semester
Educational Aims
To introduce the basic concepts, notation and terminology used in algebra. This will lay the foundation for further study in algebra and number theory.Learning Outcomes
1. 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;
2. 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;
3. 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);
4. Prove or disprove basic algebraic statements by building logical arguments and proofs, clearly and precisely expressed using standard mathematical notation;
5. State and prove simple results about groups, both for general abstract groups and for concrete examples;
6. 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.