Department of Mathematics
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Introduction to Pure Mathematics
Course G5087
Course details for 2011 cohort.
Level 1
12 credits
Autumn term
Library
Required Text:
D.L.Johnson, Elements of Logic with Numbers and Sets.
Recommended Text:
Geoff Smith, Introductory Mathematics: Algebra and Analysis, Springer.
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
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
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Term | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Equal weighting for all components. | ||
| Exercise | Autumn Week 7 (1 hour) | |
| Problem Sets | Autumn Week 1 | |
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.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Term | LECTURE | 1 hour | 111111111100 |
| Autumn Term | LECTURE | 2 hours | 111111111100 |
| Autumn Term | WORKSHOP | 1 hour | 111111111100 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Peter Giesl
Assess convenor
http://www.sussex.ac.uk/profiles/211843
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