Course Review EE 635

EE 635 – Applied Linear Algebra

Year: 2023-24 Autumn Semester
Instructor: Prof. Dwaipayan Mukherjee

Motivation

With the rise of Machine Learning and Data Science, linear algebra has become a key player in developing algorithms and models. From understanding the mathematics behind neural networks to solving optimization problems, the concepts you’ll learn in this course directly apply to the evolving landscape of technology.

Course Content

The official course content can be found here. The updated syllabus is listed below:

• Groups, Rings, Integral domains, Fields.
• Vector spaces, linear dependence, Basis, Transformation of basis, Subspaces.
• Linear transformation, Representation of linear transformations with respect to a basis, Kernel, Image, Isomorphism, Injection, Surjection, Bijection.
• Linear functionals, Dual, Double dual, Annihilator of a vector space, Dual map.
• Product spaces, Affine sets, Quotient spaces, Quotient map, Induced map.
• Inner product spaces, Gram Schimdt orthonormalization, Orthogonal complement, Orthogonal projections, Riesz representation theorem, Adjoints, Selft adjoints.
• The algebra of polynomials, matrix polynomials, annihilating polynomials, minimal polynomials, characteristic polynomials.
• Invariant subspaces, State space solution, Eigenvalues, Eigenvectors, Generalized eigenvectors, Matrix norms, Matrix diagonalization, Jordan forms.
• Application of Linear Algebra in Graph theory, Economics and other engineering domains.

Feedback on Lectures

• Teaching Style: The instructor’s teaching style fell short in terms of effectiveness and engagement. Despite excellent communication skills, the rapid pace left little time for students to absorb the material, and there was a lack of concern for student understanding. The haphazard presentation of content, without a clear order, made it challenging for students to follow a logical progression of concepts. The absence of slides further hindered the learning experience, leaving students without essential visual aids. Overall, the teaching style lacked the necessary structure and consideration for students’ comprehension.
• Attendence: Not taken.

Feedback on Assignments and Exams

• Weightage: Assignments - 15%, Quizzes - 15%, Midsem - 25%, Endsem - 45%
• Pattern: Assignments proved time-consuming, featuring a broad problem set from which 30% of the questions were repeated in subsequent assessments. Exams, particularly the Midsem and Endsem, were challenging, focusing on prove/disprove type questions that demanded a thorough understanding of the material.

Difficulty Level

This course poses a considerable challenge due to its inherently proof-oriented nature. Mastery of proofs requires significant time investment, making it a highly difficult and mathematically intensive course. Success hinges on extensive practice, particularly with questions sourced from the recommended standard books (Sheldon Axler and Hoffman Kunze). To excel, students must engage deeply with the material and tackle a variety of problem types.

Prerequisites

While no formal prerequisites are required, having prior exposure to MIT’s Linear Algebra course by Gilbert Strang can be beneficial for intuitively grasping the material. It’s important to note that there is no direct connection between the two courses, but familiarity with Strang’s course may provide a helpful foundation for understanding certain concepts in this course.

Grading Stats

Reference Books

• K. Hoffman and R. Kunze, Linear Algebra
• S. Axler, Linear Algebra Done Right

Reviewed by

Soumen Mondal (Email: 23m2157@iitb.ac.in)