20

It sounds like your students are not getting what they wanted from your tutelage; since they are not getting a formal credential from their work with you, their likeliest motivation is that they think additional math knowledge will aid them in their research projects or careers. As you said, the case-study student's objective is to learn the equivalent of a ...


16

I think the real issue here is that you thought you were essentially doing undergraduate tutoring, and you weren't. You were doing adult education, and that is not the same thing. When someone is in their 40's and has not worked - daily - with math since college...they no longer know any math. They have probably even lost much of their high school math, as ...


9

My advice (IN GENERAL) is to follow the book VERY explicitly and closely. You still should be doing lots of active things, not just "reading". But use the book as a scaffold. In self instruction, the dangers of flailing around (to include quitting) are way higher than the dangers of missing something book did not cover or not thinking for ...


6

First, let's note that the terms as used by Rosen are standard definitions, as we can see on Wikipedia (here and here), as well as other resource sites. There was some question about this in the comments, so I thought to clarify this first. Perhaps reading those articles will give an added perspective for the OP. Now, I'm not going to offer a mnemonic -- I ...


6

The American comedian Henny Youngman had this joke: The patient says, "Doctor, it hurts when I do this." The doctor says, "Then don't do that!” Unfortunately, some people have the incorrect idea that mathematics is about "solving problems", and lots of them, but it's not. The truth is that math since Euclid is about establishing ...


5

My biggest advice is not just to "see where you went wrong" or "do the FM". But redo the entire missed problems as if you had not seen the answer. Very important! IOW, after finding out your mistake and correcting it, put the old work aside, look only at the problem statement and work it fresh. (I.e. in your mind, treat it as a fresh ...


5

I am not familiar with this book, but the title alone suggests it might be worth examining for your purposes. Statistics for Mathematicians: A Rigorous First Course. Victor M. Panaretos. Compact Textbook in Mathematics. Birkhäuser/Springer 142 (2016). ISBN-10 : 9783319283395. Springer link. "Intended for students of Mathematics taking their first ...


5

This perspective is known as Formalism https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics). It is sometimes the case that working out the details of a symbolic argument is tedious and unenlightening, in which case it is easier to simply convince someone that you could in theory write out the details in a purely formal way. It is my ...


5

Organic chemists are well known for "only needing to count to 4". Sure, they have some math in their studies, but it's really not used for natural products synthetic chemists. I disagree with the commenter who said to confront the fellow, demanding proof of his professorship. If you really care, look it up yourself. But it's inappropriate to ...


4

I would suggest "All of Statistics" by Wasserman. It is reasonably concise and moderate in its demands on background, but much more mathematically serious, also covering a much wider range of material, than a typical first course in statistics.


4

After giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. I looked at the second edition (not the Gardner update), but unless Gardner practically rewrote the book I don't think this matters much. At the very beginning, ...


4

The Canvas class for Dartmouth's Spring 2020 course in Graph Theory, Math 38, seems to be mostly open. According to the syllabus, the course uses the 2nd edition of West's Introduction to Graph Theory. Course Description This course will cover the fundamental concepts of graph theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, ...


4

The fact that the book uses infinitesimals (presented informally) rather than limits is definitely a big deal, and I think you will have to read the book for yourself to see if it works for you. When I was exposed to the idea of $dx$ as some kind of infinitely small quantity, my philosophical confusion completely blocked me. But the idea of a limit, even ...


3

In a sense it is OK. In the sense that almost any book (except for one that is very difficult, and assigned to a weaker student and/or one without strong motivation to prevail) is OK. It's really more about your sticktoitiveness than anything else, what you get out of it. I'm working on a language study right now. I have several different texts available ...


3

I have this book. A lot of the problems are pretty similar and there are a lot in there. Normally, I'm in favor of doing all the exercises (since you get faster as you go). But I really don't think that quantity of drill is required for a strong student, especially since this is a course that some people still eschew (not taking any proofs class). Maybe ...


3

A few things that I find help. Make sure you have some easy drill problems at the start of a homework session. Most books are actually well set up for this approach. Having I, II, and III problems (or A, B, C). The first category are plug and chug. Last category require a little bit of derivation or more detailed word problems. Intermediate are usually ...


3

You could consider the series distributed in the United States by singaporemath.com: Primary Mathematics for grades 5 and 6 New Elementary Mathematics for grades 7 and 8. You can also find later volumes of New Elementary Mathematics for grades 9 and 10 for sale on the internet. Primary Mathematics has three versions adapted for the U.S., while New ...


3

I recommend starting him with Beast Academy (maybe even go down to their level 4 or below). Beast Academy is very fun; the rigor may not be obvious, but they are building thinking skills. When he's done with BA, then go to Art of Problem Solving.


3

See Mathematics of Choice. How to Count Without Counting by Ivan Niven (1965). For what it's worth, problems like this can be relatively straightforward with the appropriate tools (found in the book I cited) and they can be quite difficult even with a reasonable knowledge of these tools, and sometimes it's not easy to tell in advance unless one is very ...


3

It may be that his style of learning differs from yours. I have an MA in math, and when my son was in high school helped tutor him in math and physics. I always like the "aha moment" in proofs, where the purpose of previous obscure statements becomes plain. My son hates that - when I delivered the punch line he would get upset and say "where ...


2

One way to remember the mathematics that you learn is to create a narrative that explains how the concepts are threaded together. This narrative need not have any historical relevance (and it usually cannot, since historical developments are usually tangled and messy). The goal is to lay down a road from start to finish, passing through all the important ...


2

Firstly, congratulations for taking on this task. Of course it is very important to actually complete problems, rather than just read the notes. I would say that completing the odd numbers is a sensible compromise - you can go back and complete the even questions at a later date for more practice or revision. Good luck!


2

Terms to search for include "blocked practice" and "interleaving"; the latter is also known as "mixed practice" or "varied practice". For instance, see https://effectiviology.com/interleaving/ (excerpt below) Interleaving is a learning technique that involves mixing together different topics or forms of practice, in ...


2

I advise one, not two. The biggest danger with self study is quitting. Keep it simple and get an earlier victory. Will reduce quitting danger. Retention can be kept by periodic review. And/or really just brushing up, WHEN YOU NEED IT later in life. Nobody expects you to remember every trick, if you are not continuing to use the stuff and/or doing a ...


2

I enjoy teaching math, I get paid for dealing with the b.s.. If it turns out that there is more b.s. to deal with that I initially expected, my price goes up. I don't explicitly tell the client that that's the reason why the price is now higher, but I set my price to the b.s. level. So either the client pays me enough to put up with it all, or decides that ...


1

Perhaps take a look at "Linear Algebra Done Wrong" by Treil. Free PDF download, so you can take a thorough look. Others swear by Axler's "Linear Algebra Done Right", to which the previous is a reaction, but this one isn't available for free.


1

Despite the last word in the name, you might consider Bernard Kolman's Linear Algebra with Applications. Most of it is not applications and you can ignore the parts that are (tending to be at the ends of chapters or exercise sessions), and just get help with the basics. FWIW, I find it incredibly easy and gentle. Almost entirely requires no calculus, for ...


1

That book gets ripped pretty hard on Amazon. The Dover texts by Trudeau and Chartrand are supposedly easier and friendlier, per reviews. And will be cheap, since Dover. If you want to develop familiarity and speed, I would certainly not eschew (i.e. I would do) problems that are repetitive. You'll get more practiced at the concept. Also more practiced at ...


1

I don't agree that there should be a passing score when it comes to studying using problem sets if you wish to simply grind through all the problems. Should it be acceptable to have one wrong answer? If so, why would having two wrong answers not be acceptable? Three? Out of how many problems? Assuming that your problem sets all feature the same type of ...


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