Mathematics 2B: Linear Algebra
University of Glasgow
Area of Study
Taught In English
Mathematics 1R or 1X at grade D and 1S or 1T or 1Y at grade D and a pass in the level 1 Skills test.
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits2.5 - 3
Recommended U.S. Quarter Units1
Hours & Credits
This course covers the fundamentals of linear algebra that are applicable throughout science and engineering, and in particular in the physical, chemical and biological sciences, statistics and other parts of mathematics.
One degree examination (80%) (1 hour 30 mins); coursework (20%).
Main Assessment In: December
This course covers the fundamentals of linear algebra that are applicable throughout science and engineering, and in particular in the physical, chemical and biological sciences, statistics and other parts of mathematics. The aim of the first part of the course is to introduce the idea of a finite dimensional vector space, including the concepts of linear independence, basis, dimension and linear map. The relation between linear maps and matrices will be explained, and this will motivate further study of matrices in the second part of the course, in which the determinant, eigenvalues and eigenvectors of a matrix will be studied. Throughout, all new ideas will be illustrated by examples drawn from applications in low dimensions.
Intended Learning Outcomes of Course
Students should be familiar with all definitions and results covered in lectures, should understand the proofs of results, and should be able to apply the results to problems involving the course contents. Students should, moreover, learn to be rigorously logical in their presentation of solutions to problems. By the end of the course, students should be able to (1) handle fluently problems involving matrices and their entries; (2) recognise vector spaces and subspaces over R and C: (3) test sets of vectors for linear independence and spanning properties, and understand methods for obtaining bases for a specified subspace of a vector space; (4) decide whether or not a map between spaces is linear, describe a linear map in matrix form, and calculate various objects (eg image, kernel) associated with a linear map; (5) evaluate determinants recursively and using elementary row and column operations, factorize algebraic determinants, and apply results about determinants in theoretical problems; (6) find the characteristic polynomial of a square matrix, and use it to determine the eigenvalues and eigenvectors of the matrix, and deal with theoretical problems involving eigenvalues.
Courses and course hours of instruction are subject to change.
Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.
ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.
Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.