Linear Algebra
part 1 of 3

A total of 46 hours of lectures

This is an academic level course for university and college engineering. Due to its size, it is divided into three parts. This page describes the first of those three parts.

Prerequisites

High-school maths, mainly arithmetics, some trigonometry

Curriculum

Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

Linear Algebra, part 1 of 3

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Get the outline

A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.

Get Linear Algebra part 1 on Udemy

When you buy the course on Udemy, you get access to it for life. There is just a one-time fee. The prices do vary a lot on Udemy, but if you use our link by clicking on this panel, you will get the best current price. See also our page on “coupon codes” in the menu (the current code is TPOT_NOV24).

Course Objectives & Outcomes for part 1

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How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
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Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).
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Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
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Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
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Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.
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Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
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Understand the connection between systems of linear equations and matrix multiplication.
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Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
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Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
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Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer’s rule for n-by-n systems of equations.
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Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
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Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
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How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.
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Invertible Matrix Theorem and its applications; apply determinant test in various situations

Richard T.

Udemy student

J’aime beaucoup la manière dont la professeur enseigne et explique. J’apprécie la douceur du ton. Ce qui augmente mon intérêt pour l’écoute.

Farzad R.

Udemy student

Outstanding perspicuity as always.

Sayan D.

Udemy student

This course was phenomenal. Thanks Hania.

Peter D.

Udemy student

Very soothing voice, ASMR and math in one.

Matthew T.

Udemy student

She is the best. She knows her content!

Very good I wish there were more courses she taught like linear algebra 4 etc.

Long P.

Udemy student

I love the linear transformation and analytical explantions in this video. I don’t understand why some people don’t like it. Basic mechanical skills could be learned anywhere else. Truly in-depth explanations are what learners actually need.

Udemy User

Udemy student

Very concise, very clear presentation and delivery, quite suiting tone. So far, better than what I expected.

Minjun K.

Udemy student

so good~~~

Daniel S.

Udemy student

This is a splendid course in an absolutely foundational topic, with detailed explanations and examples, and presented at a gentle pace that anyone with thorough preparation in high school mathematics can easily maintain.

Roman M.

Udemy student

Hania explained everything very well and answers all questions in the Q&A. Would love to have more solved problems.

Instructor response

Thank you for the review, Roman. There are 175 problems solved in the videos, and even though it is a lot, I understand that students need an opportunity for more practice. This is why I recently (just some days ago) attached a document “how to get more practice” as a resource to Video 1. In this document you can find, among others, a link to an excellent (and free of charge) Linear Algebra book. You get there both plenty of solved examples, and exercises (with answers) to solve on your own. It is also possible to ask (me) questions about these exercises; just post a question under a video related to the subject of the exercise, and I will be happy to help.

Lisa H.

Udemy student

These courses are everthing I was looking for and even more. Up to this point I was only interested in math, but now I’m starting to love (and really unterstand!) it. Thanks for this wonderful opportunity.

Rick S.

Udemy student

Very clear description of what the course covers.

Andres C.

Udemy student

I would like to say I have learned so much based on this course! Hania Uscka-Wehlou lays out perfectly each and every section of this course. She is the best Instructor I have ever had. I’ll be looking forward to taking more mathematical courses with her later on in the future.

Rodrigo M.

Udemy student

Really nice course. Everything well explained both vocally and graphically. Step by step approach that makes a lot of sense. I wish every course was like this! Highly highly recommend and have already enrolled in the other courses Hania offers. Thank you very much for the effort of creating and publishing these courses! It’s a huge resource.

Dani

Udemy student

Amazing teacher and amazing course. This course alone is better than 99% of introductory university courses out there. In my opinion, the best way to take the most out of this course is to have a side book on linear algebra as well. Again, fantastic course and HIGHLY recommended.

Soo Ching L.

Udemy student

Very clearly explained with good illustrations. I absolutely loved this course and will not hesitate to subscribe all other courses by the same trainer.

Luca B.

Udemy student

The course is very well done. The teacher is very precise in her explanations; she explains the concepts in detail. Several exercises are done during the course to reinforce the concepts. At each lesson there is a pdf document that shows the topics covered which in my opinion is very useful. Last but not least, the teacher was always very helpful in answering my various questions that allowed me to clarify some of my doubts.

I thank the teacher for the excellent work she did.

Tyrone P.

Udemy student

Thanks for taking the time to construct your courses – It’s been 20 years since doing a comprehensive course in LinAlg (Applied Math and CompSci grad). And now refreshing my knowledge for those at the office who think Machine Learning etc is just a matter of running a program. My only point on Section 2 is to break the Linear Transformations section up a bit more why: This is typically one of the hardest concepts for people new to LinAlg to get their head around along with Linear combinations – both fundamental to the introduction of the subject. Anyhow – I have purchased your three LinAlg courses which I intend to plough through over my 4 weeks off over the Christmas period. It’s a tricky topic to deliver! Keep up the good work. Will continue to feed back.

Section 3 Nice Representations of equations and related geometrys. The nexus between the 2 is often overlooked in undergrad courses and other online instructional courses on the subject.

Ted H.

Udemy student

I am a retired engineer who is taking these courses in conjunction with a degree program at a Canadian university (for fun). I have taken many online courses and I am very selective as to which courses I purchase. I have purchased all of this professor’s courses based on their value.

Professor Uscka-Wehlou is an exceptional teacher. Her courses typically have around 50 hours of video which is more teaching time than in a typical university course. The material is very clearly presented and there is no fluff added to pad the hours. Much of the material I have taken previously many years ago, but I am filling in many of the gaps that I never learned the first time around. A valuable bonus is that Professor Uscka-Wehlou takes questions asked in the Q & A section of the course very seriously. She responds faster than you would expect and the answers are complete and explanatory. I make it a point to read all of the questions asked by other students to enhance my learning. I have benefitted tremendously from each of her courses.

Ana M.

Udemy student

Hania is the best teacher, the courses are really amazing and all of them help to understand the reason for everything in math, she is a really good and admirable teacher, the material is incredible and the way of teaching is unique. All math teachers must watch Hania’s courses before becoming math teachers. I feel very happy for finding Hania’s courses, waiting for all the future ones!

Andrea T.

Udemy student

I studied linear algebra a long time ago at university and took this course simply to refresh my knowlegde. But this course didn’t only refresh my knowledge and helped me to improve my rusty skills to manually compute things, I understood concepts and saw connections that I never really understood or saw before. It was all in all a wonderful experience. The lectures are very clear, extremly well structured and organized, easy to follow and fun to watch. I absolutely recommend this course. Thanks a lot for this wonderful couse. I will start the second course today and am really looking forward to it.

Zsdfasd

Udemy student

Excellent, wonderful, terrific, fabulous, great

Neil D.

Udemy student

If I had Hania as my grad school professor – I would have scored a lot higher than I did. I am currently pursuing math as a hobby (and to satisfy my intellectual curiosity), and even for me (who is not as invested as a student would be) – Hania brings math concepts to life. I dont “have” to take any of her courses because I am not preparing for any test – and yet I will buy all her courses in due time. I am that impressed by the efforts gone in making this LA-I course.

I so envy students nowadays who have access to such resources at such affordable price points. Make the most of it.

Mathematics is typically taught in a very dry and boring way. But not Hania. Teachers like Hania, Khan and 3Blue1Brown are putting the love for math in people’s heart – and that is no mean feat. Not many can do that – as you already know. Thanks, Hania! I look forward to more courses from you in the coming years.

Paul K.

Udemy student

Exceptional – explanations of the material, mostly by example, that are rigorous, clear, and engaging; with a polished and professional use of this online medium. While a 3 credit, semester-long course is expected to provide 45 hours of lecture and a textbook, the instructor dedicates 143 hours to teaching this subject (across 3 courses), with no textbook necessary. In the Q&A, she has published a preliminary time-line for production of a full undergraduate math curriculum: an ambitious, unique, and worthy undertaking.

Rafi Ihsan A.

Udemy student

Too good to be true, it is illegal to teach this well 🙁

Jamieson P.

Udemy student

These are the best videos on mathematics to grace humanity. Stellar.

Adrian

Udemy student

I cannot express how happy I am that I found this course. Hania is an outstanding teacher and by getting her courses you get university level lectures. Everything is wonderfully structured and very well thought out, I particularly liked the visual explanations and the fact that she took time to explain the selected proofs. I can only hope that she continues to make courses and covers other topics as well.

Abdulrzak A.

Udemy student

This course is excellent, she is truly one of the best teachers out there. You get a deep understanding of everything.

Sohail A.

Udemy student

The course is detailed yet easier to follow. Explanations are easy to understand compared to other instructors. Course preparation and presentation is professional quality which is a joy. Instructor is well spoken and the lectures are clear and concise. Looking forward to other courses by Professor Wehlou.

A triumph!

Na

Udemy student

I am at the halfway point on this course, and have enjoyed it thoroughly. The professor explains the material very clearly, with excellent use of visualizations and colored highlighting using the iPad. I’m looking forward to completing this, along with the next ones.

Tuul T.

Udemy student

Excellent course, the teacher teaches very well. The teacher explains in English very well, speaks slowly and super easy to understand.

Karim M.

Udemy student

I’m almost halfway through the course and it is beyond amazing! Hania is truly outstanding! I am a bit speechless, her lectures are simply just amazing.

Be careful because Hania might turn you into a mathematician without you realizing it.

I hope Hania continues to make more courses available on Udemy.

Sureshkumar M S.

Udemy student

Must say one of the best course available on internet on Linear Algebra. Professor has an amazing pedagogy in teaching even the tough concepts in an easy, understandable, bite sized chunks. Layout of the chapters is in such a way to gradually build the foundation and move on to harder concepts one step at a time. Some of the intuitions behind determinants, inverse of matrix, intermix of linear algebra and geometry just blew my mind. It appears lot of thinking and work has gone in to every aspect of each chapter from Professors many years on experience of teaching the subject and the kind of doubts raised by students over the years. There is ample amount of worked out examples from many different perspectives to enhance the understanding of the entire subject.

At the end of the course felt this stuff should be definitely costing way more than what it is offered. If you are a student or a professional looking out to learn Linear Algebra, this course is must. Go for it!!!