Undergraduate Course: Introduction to Mathematical Analysis (MATH08081)
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 is a first course in rigorous mathematical analysis, which is the theory underpinning calculus. In addition to developing the theory, we will reinforce techniques so that students will be confident of
applying the theory in concrete settings.
A representative outline of the course is: Real Numbers, Sequences, Infinite series, Limits, Continuous functions, Differentiation. |
| Course description |
This is a first course in mathematical analysis, which aims to bring students to an understanding of and proficiency in the following topics: Real Numbers, Sequences, Infinite series, Limits, Continuous functions, Differentiation.
There is a strong focus on rigorous mathematics, which is quite different to how mathematics is typically taught at school, and builds upon the skills developed in Introduction to Mathematics at University. Students will be supported in this, as well as provided with plenty of opportunities to practice and reinforce their calculus skills.
Note that students are expected to engage with the full breadth of learning opportunities, and not just with lectures. This includes study of preliminary material, reflection on their learning, self-study of relevant concepts, and practice of skills.
Summary of student experience: you will be consolidating and putting into practice the approaches you learn in Introduction to Mathematics at University in the context of mathematical analysis, which is a key component of a Mathematics degree programme. You will also practice and reinforce your calculus skills.
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Information for Visiting Students
| Pre-requisites | This is a Year 1 course. Visiting students should have passed courses equivalent to Introduction to Mathematics at University (MATH08078). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: 0 |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 33,
Seminar/Tutorial Hours 16.5,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
143 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework: 20%
Examination: 80%
Students must pass exam and course overall. |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S2 (April/May) | MATH08081 Introduction to Mathematical Analysis | 180 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate a conceptual understanding of the real numbers and the completeness axiom, of the concept of a limit expressed in epsilon-N language, of infinite sequences and series and their convergence properties, and be able to derive basic results using this understanding.
- Demonstrate conceptual and practical understanding of limits and continuous functions expressed in epsilon-delta language, and of differentiation, and be able to derive basic practical and theoretical results using this understanding
- Demonstrate understanding of and work with rigorous definitions of the exponential, trigonometric and logarithmic functions, and be able to derive existence and uniqueness results for very simple linear ODEs with constant coefficients.
- Independently and critically formulate strategies for construction of mathematical arguments related to the course material, for example by breaking down a problem into easier pieces, explicitly identifying sub-problems, and then synthesising the results.
- Apply mathematical knowledge and understanding to discuss and rigorously explore topics and solve standard problems in analysis, using appropriate definitions and results, applying sound logical reasoning, leading to carefully explained, coherent, well-reasoned and precise arguments expressed in appropriate mathematical language in written form.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Real numbers,completeness,sequences,series,limits,continuity,differentiation |
Contacts
| Course organiser | Dr Jonathan Hickman
Tel: (0131 6)50 5060
Email: Jonathan.Hickman@ed.ac.uk |
Course secretary | Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk |
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