Why do most introductory math textbooks not contain solutions? How can a self-learner without access to a university or professor check their work?<p>The common answer I get is solutions "rob" the student of learning. Why should the fear of the lazy student cheat those that actually attempt their work and want to see if their solution is correct?<p>Additionally, I heard the argument that "you should know" if your solutions are correct. A beginner is probably prone to subtle mistakes and may think their reasoning is rational. Thus they are probably unaware of any subtle logic errors and could easily fool themselves into thinking their proofs are correct.<p>Is it partially laziness from the authors in creating new problems for homeworks/exams? Or do people think a literal beginner in math can be their own proof checker?<p>I wouldn't want a beginner programmer writing "production ready" code without code review, so why should we expect a beginner math student to write error free proofs? What is the point in not allowing solutions?<p>As great as these text may be, I couldn't and wouldn't recommend them for the beginner. These text seem to be designed solely for a classroom where students will get assistance and feedback from TAs and professors. They seem useless for a beginner to learn on their own without outside proof checking.
I studied so much discrete math in undergrad.<p>Characteristic polynomials, rook polynomials, derangements, counting, recurrence relations, elementary number theory, elementary p-adic numbers, logic, geometric series, abstract algebra.<p>I have never needed any of it, and never faced a situation where knowledge or intuition in those topics helped me to think differently about a problem, never faced any type of computational complexity questions that I didn’t solve just by looking various things up as-needed.<p>The only thing discrete math did for me was help me boost my GRE math score to get into a good math grad program, where I switched to machine learning and MCMC topics.<p>Very occasionally you might encounter a simple permutation or combination counting argument in a paper or something, but it’s rare.<p>I enjoy discrete math, but really felt misled about it’s actual usefulness in almost any corporate software / research / engineering job.<p>If you don’t know this stuff but you can grok most basic counting arguments after looking a few things up on Wikipedia, you’ll be fine. Deeper command of these topics really doesn’t yield economic returns to your effort in almost all cases, unfortunately.
I took this class. Professor Aspnes is a great teacher and his notes are ridiculously thorough.<p>On the first day of class he told us (paraphrasing) “I never went to class in undergrad, so I don’t expect you to. But the lectures will help you on the problem sets, so I encourage you to attend.”<p>For those of us who may have had... less than thorough attendance... these notes were a real godsend!<p>He also has some for his randomized algorithms class: <a href="http://www.cs.yale.edu/homes/aspnes/classes/469/notes.pdf" rel="nofollow">http://www.cs.yale.edu/homes/aspnes/classes/469/notes.pdf</a><p>And also for his other classes which you can find here: <a href="http://www.cs.yale.edu/homes/aspnes/" rel="nofollow">http://www.cs.yale.edu/homes/aspnes/</a><p>(Professor Aspnes is now the DUS of the CS department at Yale)
I see notes like these every once in a while and I always wonder, if the material is the same, how come there isn't a unified source for all of it? Why is there a need for every professor to create their own notes that cover the same things? For example, probability theory is still the same after all these years why can't we create a one true reference for people learning it.
Not complete without some finite calculus: <a href="https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20finite%20calculus.pdf" rel="nofollow">https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%...</a>
> [Foundations and logic] Why: This is the assembly language of mathematics—the stuff at the bottom that everything else compiles to.<p>> [Basic mathematics on the real numbers] Why: You need to be able to understand, write, and prove equations and inequalities involving real numbers<p>If logic is the assembly, real numbers must be the Enterprise Java frameworks :)<p>But really, aren't they from non-discrete (continuous?) mathematics? How are they useful for computer science? Like, sure we have approximations of them on computers (floats, rationals) but aren't they mostly used for those pesky boring real-world-ish calculations? Isn't CS mostly about integers?