Undergraduate Course: Accelerated Algebra and Analysis (MATH08083)

Course Outline
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
SCQF Credits	20	ECTS Credits	10
Summary	This is an accelerated version of Linear Algebra I and Introduction to Mathematical Analysis, designed primarily for Direct Entry students in the School of Mathematics. It is both an introduction to concrete, computational linear algebra and a first course in rigorous mathematical analysis. Both of these topics are crucial requirements for later courses in both pure and applied mathematics. A representative outline of the course is: Linear Algebra: Vectors, Dot product, Matrices, Systems of linear equations, Gaussian elimination, Matrix algebra, Determinants, Kernel, Image, Rank-nullity theorem, Eigenvalues, Singular value decomposition. Analysis: Real Numbers, Sequences, Infinite series, Limits, Continuous functions, Differentiation.
Course description	This is an accelerated version of Linear Algebra I and Introduction to Mathematics at University, designed primarily for Direct Entry students in the School of Mathematics. It is both a first course in rigorous mathematical analysis and an introduction to concrete, computational linear algebra. It covers the basics of matrices, linear systems and provides an introduction to the rigorous theory of limits (epsilon-N and epsilon-delta). In the analysis part, 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. In the linear algebra part, the course will also cover a wide range of applications, both to motivate the concepts introduced, and to allow students to practice their linear algebra skills. Summary of student experience: you will be consolidating and putting into practice the approaches you are learning in Introduction to Mathematics at University in the context of mathematical analysis and linear algebra, which are key components of a Mathematics degree programme. You will also master computations in linear algebra and calculus, and be introduced to a range of applications.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations		Other requirements	None

Course Delivery Information
Not being delivered

Learning Outcomes
On completion of this course, the student will be able to: Perform basic computations, both by hand and with software, in vector and matrix algebra, understand the rank-nullity theorem and how it is used, compute determinants and inverses, kernels and images. Demonstrate an understanding of applications of the linear algebra topics covered in the course. 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 from it. 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. 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.