Linear algebra and calculus are the two most important foundational pillars on which modern mathematics is built. They are studied by almost all mathematics students at university, though typically labelled as different subjects and taught in parallel. Over time, students discover that linear algebra and calculus are inseparable (but not identical) twins that interlock to form the backbone of almost all applications of mathematics to physical and biological sciences, engineering and computer science. It is recommended that participants in the MOOC Introduction to Linear Algebra have already taken, or take in parallel, the MOOC Introduction to Calculus. All of our modern technical and electronic systems, such as the internet and search engines, on which we rely and tend to take for granted in our daily lives, work because of methods and techniques adapted from classical linear algebra. The key ideas involve vector and matrix arithmetic as well as clever methods for working around or overcoming difficulties, a form of obstacle avoidance, articulated in this course as the Conjugation Principle. This course emphasises geometric intuition, gradually introducing abstraction and algebraic and symbolic manipulation, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. Students taking Introduction to Linear Algebra will: • gain familiarity with the arithmetic of geometric vectors, which may be thought of as directed line segments that can move about freely in space, and can be combined in different ways, using vector addition, scalar multiplication and two types of multiplication, the dot and cross product, related to projections and orthogonality (first week), • develop fluency with lines and planes in space, represented by vector and Cartesian equations, and learn how to solve systems of equations, using the method of Gaussian elimination and introduction of parameters, using fields of real numbers and modular arithmetic with respect to a prime number (second week), • be introduced to and gain familiarity with matrix arithmetic, matrix inverses, the role of elementary matrices and their relationships with matrix inversion and systems of equations, calculations and theory involving determinants (third week), • be introduced to the theory of eigenvalues and eigenvectors, how they are found or approximated, and their role in diagonalisation of matrices (fourth week), • see applications to simple Markov processes and stochastic matrices, and an introduction to linear transformations, illustrated using dilation, rotation and reflection matrices (fourth week), • see a brief introduction to the arithmetic of complex numbers and discussion of the Fundamental Theorem of Algebra (fourth week).
MI
Thank you Professor Easdown. Look forward to more math courses from you
CL
Intro concepts for linear algebra taught well, but I found the modular arithmetic topics out of place for something like an intro course. The last section has applications too which is nice.
VT
This is a great course on Linear Algebra! I strongly recommend it to any Precalculus or Calculus teacher/student.
MB
I really enjoyed this course. Thanks for all the hard work in putting this course together. I took a lot longer than four weeks as I took time out to ponder it all as I went. It was fun!
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Too bad that the timing to do the exercises and assessments are unrealistic. Also, if some topics are heavily emphasized in tests, there should be at least an equivalent amount of time to explain how to solve them.
A brilliant introduction to Linear Algebra. This is an excellent course. My objective for doing the course was to refresh my knowledge of Linear Algebra as I completed my mathematics degree almost 30 years ago! I had completed the sister course entitled: Introduction to Calculus and so I thought I'd follow-on with this one. A few hopefully helpful observations: 1. The course was the right level of difficulty for me and was quite challenging in parts e.g. the section on modulo arithmetic. 2. The videos are superb - the description of Markov processes was a particular highlight. 3. The recommended timings were not accurate but this could be a reflection of my own (lack of) ability. I probably took double the recommended timing but this wasn't a particular concern. It's good to invest the time to really understand and be able to visualise the concepts. 4. I found it really helpful to have done the Introduction to Calculus course beforehand. The Linear Algebra course is much harder and at the very least, one needs to have some knowledge of basic trig to be able to understand some of the concepts. In summary, an excellent course. Brilliantly explained and a good challenge to complete.
From my perspective, as someone interested in the subject but without prior exposure, this course has been both challenging and incredibly rewarding. Professor Easdown excels in teaching and adeptly presents the materials, covering linear algebra from both geometric and arithmetic perspectives, as well as its applications. I strongly recommend treating the readings as required rather than optional, as they provide many examples of problems you would come across in the exercises. In terms of support, it's rare to find another course where the instructor is as responsive to students' questions as this one. Many MOOCs often leave you feeling isolated, navigating through materials alone. However, in both this course and the Intro to Calculus class I previously took with Professor Easdown, he consistently engages with students' queries in the discussion forums. His dedication makes this course as close to a traditional classroom experience as you can get online.
Professor Easdown has an obvious passion for mathematics and it shows. I truly enjoyed every single one of his courses. It is rare to find a professor who can make advanced mathematics so accessible and easy for the student to understand. Each lesson really builds on the next in a logical progression, and the course structure is simple and straightforward. I used these courses to help review my undergraduate mathematics before starting graduate school and found them incredibly helpful.
Grazie mille per questo corso bellissimo. Grazie al professore! Thank you very much for this beautiful course!
This course teaches you from the ground up for solid foundation. Hidden challenge problems are included in the few last problems of each assignments. Recommend for those who need to build up knowledge from the basic to prepare for more advanced courses.
I really enjoyed this course. Thanks for all the hard work in putting this course together. I took a lot longer than four weeks as I took time out to ponder it all as I went. It was fun!
Excellent, challenging course. I had a lot of fun, thank you Prof. Easdown, and I am looking forward to taking your next courses!
This is a great course on Linear Algebra! I strongly recommend it to any Precalculus or Calculus teacher/student.
Данный курс дает новый взгляд на задачи линейной алгебры, что примечательно, все задачи имеют приложение
Thank you Professor Easdown. Look forward to more math courses from you
wow this is a challenging class. some number theory unexpectantly thrown in. Markov processes also. a lot of geometry. but feels like I accomplished something when I finished it. Definitely know more about subject as a result of taking this class; the professor was enthusiastic, videos very helpful.
This was a very detailed course, and took me longer than any other EVER - not because it was difficult, but so detailed and SOOOO many mandatory quiz questions. The advanced Calculus course is similar in style and workload.
Intro concepts for linear algebra taught well, but I found the modular arithmetic topics out of place for something like an intro course. The last section has applications too which is nice.