Undergraduate Course: Fundamentals of Pure Mathematics (MATH08064)
|School||School of Mathematics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
|Home subject area||Mathematics
||Other subject area||None
||Taught in Gaelic?||No
|Course description||This is a first course in real analysis and a concrete introduction to group theory and the mathematics of symmetry.
Information for Visiting Students
|Displayed in Visiting Students Prospectus?||No
Course Delivery Information
|Delivery period: 2013/14 Semester 2, Available to all students (SV1)
||Learn enabled: Yes
|Course Start Date
|Breakdown of Learning and Teaching activities (Further Info)
Lecture Hours 44,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
Students must pass exam and course overall.
|Breakdown of Assessment Methods (Further Info)
|Main Exam Diet S2 (April/May)||Fundamentals of Pure Mathematics||3:00|
|Resit Exam Diet (August)||Fundamentals of Pure Mathematics||3:00|
Summary of Intended Learning Outcomes
|1. Perform basic set manipulation and to distinguish between common countable and uncountable sets
2. Using straightforward epsilon methods to establish convergence/non convergence of sequences.
3. Verifying limits of functions and check continuity using the epsilon-delta method.
4. Computing derivatives from first principles, and by manipulation rules.
5. Performing simple proofs using epsilon-delta techniques.
6. Using the following tests to check convergence/non-convergence of series: comparison, ratio, root, integral, alternating series and understand absolute convergence.
7. Familiarity with the language and ideas of basic group theory.
8. Ability to calculate in several different sorts of group.
9. Familiarity with the language and ideas of group actions.
10. A knowledge of the basic theorems in group theory mentioned in the syllabus
11. Ability to apply these theorems to solve combinatorial problems involving symmetry.
|See 'Breakdown of Assessment Methods' and 'Additional Notes' above.|
Week 1-2: Real numbers and sets (including inequalities, supremum, and countability)
Week 3-4: Real sequences (from limits to Bolzano-Weierstrass theorem)
Week 5-6: Continuity (from limits for real-valued functions to continuity, including extreme value and intermediate value theorems)
Week 7-9: Differentiability (from the definition to the mean value theorem and inverse function theorem)
Week 10-11: Series (including the definition, integral (without proof), comparison, and ratio tests).
Week 1: Symmetries of squares and circles (Chapter 1)
Week 2: Permutations (Chapter 2)
Weeks 3-4: Linear transformations and matrices. The group axioms. Subgroups. (Chapters 3-5)
Week 5: Cyclic groups (Chapter 6)
Week 6: Group actions (Chapter 7)
Week 7: Equivalence relations and modular arithmetic (Chapter 8)
Week 8: Homomorphisms and isomorphisms (Chapter 9)
Week 9: Cosets and Lagrange's Theorem (Chapter 10)
Week 10: The orbit-stabiliser theorem (Chapter 11)
Week 11: Colouring problems (Chapter 12)
||Analysis: Students are expected to have a personal copy of: An Introduction to Analysis by W. R. Wade. (This book is also relevant for Y3 courses.)
Group theory: Students are expected to have a personal copy of:
Groups, by C. R. Jordan and D. A. Jordan
|Course organiser||Dr Martin Dindos
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427
© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am