Undergraduate Course: Proofs and Problem Solving (MATH08059)
Course Outline
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 
SCQF Credits  20 
ECTS Credits  10 
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. 
Course description 
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.
10. Permutations.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  Higher Mathematics or Alevel at Grade A, or equivalent 
Information for Visiting Students
Prerequisites  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? 
Yes 
Course Delivery Information

Academic year 2021/22, 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 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
135 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

Assessment (Further Info) 
Written Exam
50 %,
Coursework
50 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 50%, Examination 50% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
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  
Learning Outcomes
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.

Reading List
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. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  PPS 
Contacts
Course organiser  Prof Christopher Sangwin
Tel: (0131 6)50 5966
Email: C.J.Sangwin@ed.ac.uk 
Course secretary  Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk 

