Undergraduate Course: Proofs and Problem Solving (MATH08059)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
||Availability||Available to all students
|Summary||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.
This syllabus is for guidance purposes only:
1. Sets, proofs quantifiers, real numbers, rationals and irrationals.
2. Inequalities, roots and powers, induction.
3. Convergent sequences
4. Least upper bounds. Monotone Convergence. Decimals.
5. Complex numbers, roots of unity, polynomial equations, fundamental theorem of algebra.
6. Euclidean algorithm, prime factorization, prime numbers.
7. Congruence, primality testing.
8. Counting and choosing, binominal coefficients, more set theory.
9. Equivalence relations, functions.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| Higher Mathematics or A-level at Grade A, or equivalent
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2021/22, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 30,
Seminar/Tutorial Hours 15,
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
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 50%, Examination 50%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||(MATH08059) Proofs and Problem Solving||2:00|
|Resit Exam Diet (August)||(MATH08059) Proofs and Problem Solving||2:00|
On completion of this course, the student will be able to:
- Show an appreciation of the axiomatic method and an understanding of terms such as 'Definition', 'Theorem' and 'Proof'.
- Read and understand Pure Mathematics written at undergraduate level, including 'Definitions', 'Theorems' and 'Proofs'.
- Write clear meaningful mathematics using appropriate terms and notation and to analyse critically elementary Pure Mathematics presented or written by themselves or others.
- Understand and be able to work with the fundamental ingredients of sets, and functions between sets, and the basic properties of number systems.
- Solve standard and 'unseen' problems based on the material of the course.
|Students will require a copy of the course textbook. This is currently "A Concise Introduction to Pure Mathematics" by Martin Liebeck. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.|
|Graduate Attributes and Skills
|Course organiser||Prof Christopher Sangwin
Tel: (0131 6)50 5966
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050