Undergraduate Course: Accelerated Proofs and Problem Solving (MATH08071)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
||Availability||Not available to visiting students
|Summary||This course is an accelerated version of 'Proofs and Problem Solving' course, intended only for students on the accelerated programme (direct entry to year 2) and students on combined degrees who cannot take that course in their first year. The syllabus is similar to that for 'Proofs and Problem Solving', but some topics less essential to further study are omitted or treated more quickly.
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)
|Prohibited Combinations|| Students MUST NOT also be taking
Proofs and Problem Solving (MATH08059)
||Other requirements|| This course is an accelerated version of 'Proofs and Problem Solving' course, intended only for students on the accelerated programme (direct entry to year 2) and students on combined degrees who cannot take that course in their first year.
Course Delivery Information
|Academic year 2020/21, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 11,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
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 S1 (December)||2:00|
|Resit Exam Diet (August)||2:00|
On completion of this course, the student will be able to:
- Read Pure Mathematics written at undergraduate level, including 'Definitions', 'Theorems' and 'Proofs' and demonstrate understanding of the key ideas.
- Write clear meaningful mathematics using appropriate terms and notation and analyse critically elementary Pure Mathematics presented or written by themselves or others.
- Be able to work with the fundamental ingredients of sets, and functions between sets, and the basic properties of number systems.
- Solve standard and unfamiliar problems on the material taught in the course and using methods developed in the course.
|Students will be assumed to have acquired their personal copy of|
A Concise Introduction to Pure Mathematics, by Martin Liebeck, 4th Ed. 201, CRC Press, £29.99, on which the course will be based. (3rd Ed. will also be acceptable).
|Graduate Attributes and Skills
|Course organiser||Dr Milena Hering
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427