Key facts
Details for course being taught in current academic year
Level 1 - 12 credits - autumn term
E-learning links
Resources
Course description
Course outline
1. Numbers; introduction of mathematical symbols; natural numbers, integers, rationals, real numbers, roots; decimals.
2. Concept of proof; logical argument; theorem, lemma, corollary, proof by contradiction.
3. Set theory: union, intersection, difference; general properties of sets; examplees: N, Z, R
4. Induction: examples: n!, “n choose k’, binomial formula
5. Inequalities; axioms of order, comparison of numbers; the modulous (absolute value), triangle inequality
6. Archimedian axiom; integer part of a real number; consequences of Archimedian axiom.
7. Functions: bijection, injection, surjection; equivalence relations; countable and uncountable sets.
8. Sequences of real numbers; properties, examplse; convergence
Learning outcomes
By the end of the course, a successful student should be able to:
1. Demonstrate knowledge of various styles of mathematical proof.
2. Show knowledge of fundamental properties of real numbers
3. Prove mathematical statements
4. Show knowledge of fundamental properties of sequences and limits
5. Demonstrate skills in basic techniques
Library
Required Text:
D.L.Johnson, Elements of Logic with Numbers and Sets.
Recommended Text:
Geoff Smith, Introductory Mathematics: Algebra and Analysis, Springer.
Assessments
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 20.00% | |
| Problem Sets | Autumn Week 1 | equal weighting |
| Exercise | Autumn Week 7 (1 hour ) | equal weighting |
| Unseen Examination | Summer Term (1 hour 30 minutes) | 80.00% |
Resit mode of assessment
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Vacation (1 hour 30 minutes) | 100.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
Teaching methods
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Term | LECTURE | 1 hour | 1111111111 |
| Autumn Term | LECTURE | 2 hours | 1111111111 |
| Autumn Term | WORKSHOP | 1 hour | 1111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.