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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Proofs and Problem Solving (MATH08059)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryThis 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.
Course description 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)
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1b (MATH08075) OR Mathematics for the Natural Sciences 1b (MATH08073)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2015/16, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( 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 130 )
Additional Information (Learning and Teaching) Students must pass exam and course overall.
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)(MATH08059) Proofs and Problem Solving3:00
Resit Exam Diet (August)(MATH08059) Proofs and Problem Solving3:00
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.
Reading List
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.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr David Jordan
Tel: (0131 6)50 7210
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
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