In this 10-minutes long video I (Hania) tell you about my journey from the classroom, via Zoom, to recording courses and publishing them online. In the video I speak Swedish, but there are subtitles in English and in Polish. In this video you can see my work place. Nowadays I use it for recording our courses for Udemy.

# Hania on distance teaching in mathematics

by Hania Uscka-Wehlou | Oct 22, 2021 | courses, university mathematics | 18 comments

Hi Hania,

I would just like to know if there will be a pre-calculus course planned?

I’m a software engineer but last studied maths around 22 years ago but I am looking to start again. I’m mostly interested in calculus and linear algebra but obviously very rusty in the basics.

Is calculus required for your Udemy course Linear Algebra and Geometry 1? I often see that calculus is mentioned as a prerequisite for linear algebra even though I am not sure why.

Thank you and best regards,

Andy

Hi Andy,

Our first Precalculus course is published (yesterday evening). If you wish to purchase it, you are very welcome to use this link leading to a reduced price:

https://www.udemy.com/course/precalculus-1/?couponCode=TPOT_FEB22

The content of this course can be seen here:

http://www.wehlou.com/hania/files/uu/Outline_Precalculus1.pdf

Kind regards,

Hania

Hi Andy,

Thank you for your questions. I have only good answers ðŸ™‚

1. I am actually working now on my first precalculus course. It should be released in several weeks. This first part is called “Basic notions” and it is a kind of bridge between high school maths and university maths. Also perfect for somebody who needs to brush up on his knowledge of the subject. Afterwards there will be Precalculus 2 (Polynomials and rational functions), Precalculus 3 (Trigonometry) and Precalculus 4 (Exponential and logarithmic functions). When I am done with these four courses, I will record Calculus 1 and 2.

2. You don’t need any Calculus for Linear Algebra and Geometry 1. Not at all. I have some examples of applications of systems of equations in Calculus, but it is just two videos of 200+, so it is almost nothing. “Some calculus” is mentioned in the next linear algebra courses because there are more examples from Calculus in these courses. But you can follow the rest of the courses if you don’t remember Calculus (or you can watch the videos with examples from Calculus and refresh your memory). You should also know that my Linear Algebra and Geometry 1 contains quite

a few videos covering the prerequisites, which is always good for students who had a break from maths.

Kind regards,

Hania

Hi Hania,

I last studied math in my computer science undergraduate degree, but unfortunately (as my current master studies have revealed) the CS curriculum in the university I studied at (a university in the UK) didn’t get too involved into math and only touched on stuff what was deemed important specifically for CS. The downside of that is that without a very solid background in math a lot of very interesting master and doctorate study areas seem out of reach.

Your courses have helped me enormously in getting up to speed with the math needed for my master studies. I have really enjoyed your teaching style, presentation, problem solving examples and especially the depth in which you cover the topics, that’s one thing that really sets your courses apart from others on the same topics. I am super excited to hear that you have so many more courses in the works and I can’t wait for them to be completed. Very exciting!

Thanks for all your hard work, it really helps people.

All the best

A.D

Hi A.D,

Thank you for your kind message. It is always a pleasure to hear that our work is appreciated and that it helps other people.

I wish you all the best with your studies!

Kind regards,

Hania

I am pretty thankful for COVID-19 as it allowed professor Hania to be able to explore the idea of using tech to record high-quality lectures in mathematics: a crucial subject in pretty much everything we do. I love maths since school but the level of rigor was lacking. Even though I could get the picture of the mathematical idea, I felt something that kept bumping up in my head and bothering me. I revised lots of books. But at some point, the notation and level of detail became a nightmare to me. Then, I decided to go for free online courses. I found MIT OpenCourseWare. First, I took chemistry. I loved it as I could understand nearly everything. Then, I enrolled at Single Variable Calculus, but I felt at some level the rigor and exercises were simple. Finally, I took Multivariable Calculus. The course was great. I did understand the concepts and did a lot of exercises. Nonetheless, when I grabbed an MVC book the concepts contained a lot of notation and mathematical details I could not get my head around. Furthermore, if I got stuck, I should give up even after doing lots of research because of the complexity and time. . I panicked. So I try to find more rigorous courses in mathematics. But this time in Linear Algebra with Professor Hania. Now, I am more confident in that sense. The lectures are also well structured and geometrical pictures are richer and more meaningful. Feedback is also there at your disposal so you can feel you can master a topic you were doubtful about even before starting. Now, I appreciate maths in more depth than ever. Last but not least, I am no longer afraid of grabbing an advanced book and setting out to understand it. . I know the dynamics of how mathematics works at a high level.

Thanks, professor Hania from the bottom of my heart. Words are not enough to describe my gratitude.

Dear Derick,

Thank you so much for this beautiful message, and for sharing your experience with us.

It is such a pleasure to get appreciation and gratitude. And it is absolutely great to be able to share my knowledge with the students all around the world. Actually, nothing of this would ever happen without encouragement and help I got from Martin; I would never be able to get it right technically, and even if I did, I wouldn’t dare to teach in English (yes, in June 2020 I planned to record Calculus 3 in Swedish, as this was the language I used every day, also for teaching students, while my knowledge of English was rather passive, but Martin convinced me to create the course in English anyway, and I am very glad that I did).

I am really happy that my courses helped you advance in mathematics and that they gave you the courage for reaching for advanced books. And thank you for active participation in our courses. Your questions and remarks make them more complete and interesting for other students.

Kind regards,

Hania

Hello I’m currently working on precalculus 1 and 2 through Udemy and was wondering if you had an estimate on when 3 and 4 may be published? Thank you so much for all your efforts.

Nevermind ðŸ˜… just saw your answer about hoping to publish them in October and December respectively from another thread. Thank you again!

Hi Gray,

Right now I believe that it will rather be: November and January respectively ðŸ™‚ — there is so much I want to include in these courses!

Kind regards,

Hania

Well I throughly enjoy your in depth courses, and believe the theory is crucial to a more fundamental understanding. So I don’t blame you! I am taking calculus 2 this spring after leaving school 5 years ago (more like 8 years since I took calculus 1 ðŸ˜…). I don’t believe you will have that course uploaded by then, but am curious of your best suggestion for an online resource to review Calc 1?

Hi Gray,

Hmmm… Calculus 1 online? I have honestly no idea…

My best guess is Khan Academy, as they usually have quality stuff, no “Maths-Cookbook courses”.

3Blue1Brown for the intuition and geometry behind Calculus (no solved problems, though!).

A pretty nice place is this one https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx, but it is just text (plenty of good examples, though!).

Video lectures: I really love Travis Kowalski (https://www.youtube.com/user/TravisKowalski/playlists) but he seems to have no complete Calc 1 playlist (his Calc 3 is marvellous!)

I hope that this helps. I am still deep in Trigonometry, so Calc 1+2 must wait ðŸ™‚

Kind regards,

Hania

Do you have any ETA on the latest course that you’re working on ?

Thanks,

Nick

We’re aiming for late august. If we’re lucky, it could be earlier.

Calculus 1 and 2 when?

Calculus 1, part 1 in August, part 2 two or three months later. Calculus 2 part 1 and part 2 after that with two or three months for each.

Do you plan on doing a proof writing and/or possibly a real analysis course?

A Probability Theory/ Mathematical Statistics course would also be greatly appreciated

Hi Theo,

Thank you for your questions.

1. Proof writing: you can have a look at Section 11 in “Precalculus 1: Basic notions”:

https://www.wehlou.com/hania/files/uu/Outline_Precalculus1.pdf (the outline)

https://www.udemy.com/course/precalculus-1/?couponCode=TPOT_MAR24 (a link to the course with our discount code for March 2024)

The most important proof techniques are discussed there (Section 7: Logic, gives a preparation for Section 11).

We have also a free course on proofs by induction:

https://www.udemy.com/course/proofs-by-induction/?referralCode=5C8B2F9F4F55B813E725

More about proof techniques (partly overlapping with the material already covered in Precalculus 1) will be taught in our upcoming course on Discrete Mathematics (2025 or 2026).

2. Real Analysis: our Calculus series has elements of Real Analysis. Mostly in the first part of Calculus 1:

https://www.wehlou.com/hania/files/uu/Outline_Calculus1_part1.pdf (the outline)

https://www.udemy.com/course/calculus-1-p1/?couponCode=TPOT_MAR24 (a link to the course with our discount code for March 2024)

and in the second part of Calculus 2 (planned for the end of 2024): sequences and series, metric spaces, Cauchy sequences, maybe sequences and series of functions, but I haven’t decided yet.

For the moment I don’t plan any separate course on Real Analysis, because our Calculus series covers (or: will cover) the most important aspects of this subject.

3. Probability Theory/Mathematical Statistic: Probably (he he) not, sorry! The closest Probability Theory I will some is elements of combinatorics planned for our upcoming (2025? 2026?) course on Discrete Mathematics.

Kind regards,

Hania