There needs to be more resources for self-learning. Solutions need to be provided for problems, with clear explanations. It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention.
Funny you say that. I recently picked up a textbook on Corporate Finance for self-learning purposes. Going through the problem sets, it's not really that useful if you have no idea if you got the answer right or not. Looked all around online for where to buy the solutions manual, ended up just calling the publisher to ask. Turns out they refuse to sell the solutions manual to anyone not a registered instructor at a University.
It took like 5 minutes on the phone to even explain to them that I'm reading the book for self learning purposes. Like they'd never encountered such a thing. Even after explaining, they wouldn't let me have the solutions.
I ended up just going on the black market, and finding some anonymous person to sell me the solutions on WhatsApp for $25.
I just googled, and by the way when you want to google for something with qustionable legality, it's best to use search engines not based in western countries, such as Yandex. There ended up being a lot of sites advertising the solutions manual for sale. But also, there are entire subreddits where these people post threads advertising that they have whatever ebook/solutions for sale with a whatsapp phone number included in the content. I messaged on Whatsapp and sent a paypal payment (yes, I had no recourse, it was a leap of faith) but it's not that much a risk since it's only $25.
Agreed. It's frustrating to solve a problem and being unable to check if it is correct. It's even more frustrating knowing that if you had the answer, it would help you to solve the problem. Sometimes the answer pushes you in the right direction to figure out how to solve the problem.
> with clear explanations.
Hopefully separate from the answers.
For programming exercises, we should be given datasets so that we can tests whether our code works or not. Heck books should provide links to unit tests.
I'd go a bit deeper: as we developed, in particular with the advent of the Internet, we went from scarcity of information to spectacular opulence. This demands different studying habits that what we had 30 years ago or so.
For example, we need to find ways to filter out noise from signal, or to connect scattered bits of knowledge from various sources to get intelligible solutions to problems (most problems can be solved by googling around, especially in maths/physics, because people of all levels have been asking/answering questions for Internet points e.g. on Stack Exchange & cie for many years now, but — take it as a feature — you have to work a little to get there).
EDIT: regarding solutions, it's not just about preventing cheating, it's because teachers wants you to do the work. The point isn't necessarily to succeed in solving problems, but more to have you try, get creative, etc.
Perseverance is crucial to move forwards. But they could still provide clear and/or progressive solutions, I fully agree.
I'd really like a Khan Academy-like site, maybe with explanations from different textbooks for each concept. Of course then you'd need a good set of diverse problems or a way to generate such problems.
It's a shame that Khan has gotten less diverse in subjects. They used to have medicine and bio stuff among others, but now it's mostly maths. The maths lectures and exercises are still great, but even those seem limited (still no discrete maths last time I looked).
A Textbook is good enough for self learning. Almost all university learning is "self learning", at least that has been the case for my mathematical training.
> It's a different mindset from a formal academic setting, where there's a strong focus on cheating prevention.
What? Who cares about cheating prevention, most of my classes had oral exams, you can't cheat there.
These were master and late Bachelor courses, so 30 people at most. Exams lasted around 60 minutes, of which around 45 were questions.
>how many questions are asked?
Totally depends on the subject and how the exam goes.
>What's it like in general?
Your professor is poking you with questions. Usually he has prepared some general questions and then asks follow ups. It might go something like this. "What is X Theorem? What does it represent geometrically? Does conditions Z need to be true for the Theorems to hold? Can you name a counter example? How does the proof (discussed in lecture) look like? How exactly do you construct that part? Where do you need that condition? Here is a similar theorem (not discussed in class), can you outline a proof for this?"
I agree with you. It's been my experience though that tracking down solutions manuals for textbooks is very hard. Presumably because they want them out of the hands of students (to prevent cheating).
Have you tried to read any of the literature on the Risch algorithm? If you haven't, you might want to get started by taking a look at the paper "Integration in Finite Terms" by Rosenlicht [1] and chasing down some of the references mentioned in [2].
Of course, in the real world we don't give up on integrals just because they can't be expressed in terms of elementary functions. Usually we also check if the result happens to be a hypergeometric function, such as a Bessel function. If you want to get started on understanding hypergeometric functions, maybe try reading [3] (as well as the tangentially related book "A = B" [4]).
I hate when I buy an interesting math book and then it's like "oh wait, no solutions." And then I end up going on GitHub hoping for community-worked solutions.
