Undergraduate Course: Proofs and Problem Solving (MATH08059)
|School||School of Mathematics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
|Home subject area||Mathematics
||Other subject area||None
||Taught in Gaelic?||No
|Course description||This course is designed to introduce and develop the fundamental skills needed for advanced study in Pure Mathematics. The precise language of professional mathematicians is introduced and the skills needed to read, interpret and use it are developed.
The 'Axiomatic Method' will be developed along with its principal ingredients of 'Definition' (a statement of what a term is to mean), 'Theorem' (something that inevitably follows from the definitions) and 'Proof' (a logical argument that establishes the truth of a theorem).
Constructing proofs, and much other mathematical practice relies on the difficult art of 'Problem Solving' which is the other main theme of the course. Facility comes only with practice, and students will be expected to engage with many problems during the course.
The principal areas of study which are both essential foundations to Mathematics and which serve to develop the skills mentioned above are sets and functions, and number systems and their fundamental properties.
Information for Visiting Students
|Displayed in Visiting Students Prospectus?||Yes
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 30,
Seminar/Tutorial Hours 20,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Revision Session 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)||Proofs and Problem Solving (MATH08059)||3:00|
|Resit Exam Diet (August)||Proofs and Problem Solving (MATH08059)||3:00|
Summary of Intended Learning Outcomes
|- Appreciation of the axiomatic method and an understanding of terms such as 'Definition', 'Theorem' and 'Proof'.
- The ability to read and understand Pure Mathematics written at undergraduate level, including 'Definitions', 'Theorems' and 'Proofs'.
- The ability to write clear meaningful mathematics using appropriate terms and notation.
- The ability critically to analyse elementary Pure Mathematics presented or written by oneself or others.
- An improved facility in solving both standard problems and 'unseen' problems on the material of the course.
- Familiarity with the fundamental ingredients of sets and functions between sets.
- Familiarity with the basic properties of number systems.
- Familiarity with other material that may be presented to illustrate the principles of the course.
|See 'Breakdown of Assessment Methods' and 'Additional Notes' above.|
||This syllabus is for guidance purposes only :
Based on three lectures per week plus a two-hour tutorial. (30 lectures, to allow some flexibility in introducing the course, etc.).
The topics refer to chapters of Liebeck's book. The only omissions are complex numbers and permutations. Indicative timings (in lectures) and details of any omissions from those chapters,
etc, to be finalised when the course is designed.
- Sets and proofs (2)
- Number systems (2)
- Decimals (1)
- Inequalities, n-th roots and powers (2)
- Polynomial equations (2)
- Induction (1)
- Euler's formula (1)
- Introduction to Analysis (2)
- The integers (2)
- Prime Factorization (1)
- More on prime numbers (1)
- Congruence of integers (2.5)
- More on congruence (2.5)
- Secret codes (1)
- Counting and choosing (2)
- More on sets (1)
- Equivalence relations (1)
- Functions (2)
- Infinity (1)
||Students will be assumed to have acquired their personal copy of
A Concise Introduction to Pure Mathematics, by Martin Liebeck, 3rd Ed. 2011, CRC Press, £25.99, on which the course will be based.
|Course organiser||Dr Ivan Cheltsov
Tel: (0131 6)50 5060
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050
© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am