...

[Gil]

*poof*

Edited December 1, 2018 by Gil
Privacy

[seaben]

Where are you stopping in the curriculum?

[regentrude]

4 hours ago, Gil said:

tSo far, to me physics is a niche tool only needed to solve specific kinds of problem--which are only encountered by a limited number of fields and professions. Math reaches every thing.

I am completely puzzled by this comment. Physics is everywhere in everybody's everyday life. How a ball flies, how a car drives around a curve, how it stops, how the Earth revolves around the sun, ,why there are seasons and tides,  how your computer and your stereo work, how your cells let the sodium and potassium ions in and out, how your brain tells your foot to move, how your eye sees, how a telescope works... how is that "niche" and doesn't reach everything? Every object, every organism, every cell and cell organelle, every planet and every elementary particle is subject to the laws of physics.

ETA: I would not stop math. I would seek out resources to learn math off the beaten path. Have you completed AoPS' number theory and counting&probability? Great topics, books written to the student so that no outside instructor is necessary.

Edited October 27, 2018 by regentrude

[regentrude]

5 hours ago, Gil said:

At this level of material, prepping, teaching and grading their math class has become a part time job for me, and I'm having trouble justifying and sustaining the time and energy that I'm putting in for such small returns.

Can you explain what you mean by "such small returns"? Either they understand and learn what you teach them, and then the return is huge. Or they don't, or only through a tremendous effort on your part, because the material is not developmentally appropriate - in which case I would question what the point of this relentless acceleration is supposed to be.

[arliemaria]

Could they do Khan Academy for awhile? Maybe you just need a break, but I can't imagine taking an entire year of math off. Is it possible to outsource to a tutor at the local community college, etc.?

[Gil]

4 hours ago, seaben said:

Where are you stopping in the curriculum?

Post-calculus 3. By the end of December, they'll be 11 and 12 and will have completed

4 full passes of Algebra 1, 2 and 3 (where 3 is precalculus) 
3 full passes of plane and analytic Geometry and Trigonometry
2 passes of a course in discrete mathematics, Undergraduate Calculus (meaning all the material from a calculus 1, 2 and 3 course) and Differential equations
1 full pass through a basic course in linear algebra, and Engineering Mathematics
and most of a course on mathematical proofs/analysis, and Statistics.

We'll definitely revisit Linear Algebra and Engineering Mathematics and I know that I haven't been able to do justice to the Mathematical Proofs and Analysis, so they'll definitely need to revisit those topics in future years. I'm saving Numerical Modeling until later, on purpose.

Those are the courses where we've used a dedicated book and worked pretty much cover to cover, working all the "standard" topics and several of the "enrichment" sections also.
But over the years, we've worked select chapters or units from a number of other math books over the years.

[arliemaria]

24 minutes ago, Gil said:

Post-calculus 3. By the end of December, they'll be 11 and 12 and will have completed

4 full passes of Algebra 1, 2 and 3 (where 3 is precalculus) 
3 full passes of plane and analytic Geometry and Trigonometry
2 passes of a course in discrete mathematics, Undergraduate Calculus (meaning all the material from a calculus 1, 2 and 3 course) and Differential equations
1 full pass through a basic course in linear algebra, and Engineering Mathematics
and most of a course on mathematical proofs/analysis, and Statistics.

We'll definitely revisit Linear Algebra and Engineering Mathematics and I know that I haven't been able to do justice to the Mathematical Proofs and Analysis, so they'll definitely need to revisit those topics in future years. I'm saving Numerical Modeling until later, on purpose.

Those are the courses where we've used a dedicated book and worked pretty much cover to cover, working all the "standard" topics and several of the "enrichment" sections also.
But over the years, we've worked select chapters or units from a number of other math books over the years.

That's impressive for sure, Gil. I’d be looking into tutors or college courses. What about Physics? Or the online open MIT courses? Or a deep science/engineering project to apply the math they’ve learned this year. They are old enough for Broadcom MASTERS.

[Gil]

poof

Edited December 1, 2018 by Gil
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[mumto2]

We made several passes through most math topics in an effort to slow my kids down so I understand what you are saying but I would want them doing math for an hour or so a day.  It is easy to get out of the habit. 

My kids were not fans of AOPS either so used it as prep for math competitions but otherwise ignored it.  We always did the LoF book first for topics after we discovered them because my kids really loved Fred and I know there is now at least one book beyond Linear Algebra, that might be a fun option.  Dd always enjoyed applications books like Lial’s Applications in Calculus because she enjoyed seeing how Calculus is applied  in many fields.  Yes, it is treading water but in a way a bit extra is learned.  I know we several applications books.  

[Gil]

*poof*

Edited December 1, 2018 by Gil
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[mom2bee]

Well, they're already several years and grades ahead of the standard curve, next year seems like a reasonable place to pause, provided that you'll have them review the material that they've covered throughout the year.

Honestly, it sounds like you're dreading the change almost as much as, or more than teaching physics. Any particular reason why you're even trying to teach physics next year?

Edited October 28, 2018 by mom2bee
curb --> curve

[daijobu]

On 10/27/2018 at 7:11 PM, Gil said:

"Prep work" includes the time it takes for me to

• read and work through the lesson cold,
• read and understand, then copy and annotate any and all formulas or theorems,
• read and rephrase explanatory paragraphs to ensure I have the lesson down and can explain it,
• take notes on the material
• write out and study the textbooks examples to use during The Boys lesson, (the books may sometimes skip steps. I always try and have the complete solution.
• etc., etc. 

WOW.  I would just open the AoPS book each morning cold and wing it as we went along, reading it for the very first time when I read it out loud to them.  Finally (at around intermed. algebra or precalc) they started to get annoyed at me and insisted that I do the introductory problems in advance, so I started actually doing some prep work, but I guess I'm lazy.   My kids would've loved having you teach.  

[lewelma]

Gil, have you considered allowing them to self teach?  They are young, so you would need to supervise in some manner, but self-teaching is such an awesome skill. During high school, my son designed his own math courses, set goals, managed his work load, self-taught, and self-managed.  He did NOT do this in 7th grade, but it might be a goal you work towards for 10th. The person we need to get onto this thread is Butler.  Is she still around?  Her kid was crazy accelerated like yours. Her and Quark.  

You have accomplished so much and in a difficult environment.  My hat goes off to you!  Please take care of yourself so that you can still care for and education your boys without burning out!  You are doing an awesome job!

 

Edited October 29, 2018 by lewelma

[mathnerd]

Your sons are way ahead of even where you envisioned them to be at this age! I think that you need a break from that level of prep work. It is a good idea to not take a complete break from math. How about finding ways in which they can apply their mathematical knowledge to problem solving? Some ideas are solving competition math problems (self paced and solutions available online in case they need to validate answers), computer programming using various algorithms and data structures (they can work on their own on a long term project), mathematical logic study etc. I am sure that posters like Kathy will be along to give you more ideas. But, I cannot envision prepping to that level to teach any subject and the maximum that I have done so far is to use multiple resources and winging it! 

As lewelma said, you are an awesome math teacher! Take care.

 

[kiana]

I like the self-teaching or reading idea. Some subjects are highly conducive to this. There are also some books designed for self-study where there are fully worked solutions available.

History of Math (there are some really good resources out there now) might be interesting. There are some hoary old classics, such as E.T. Bell's Men of Mathematics, which (as a product of its times) has problems with several -isms, and yet has inspired multiple highly regarded mathematicians. There are many newer books as well. Stephen Hawking has "God Created the Integers", which leads interested readers through several genuine masterpieces (full disclosure -- this is still on my amazon wishlist). Ian Stewart has a LOT of good books. Kline's Mathematics and the Physical World would be an interesting segue into physics before you go for a full-fledged course -- they're beyond the math in it, I'm sure, but it goes through a lot of applications. It's also a Dover book so it's super cheap. Kline's Mathematical Thought from Ancient to Modern Times is also a great mathematical history. I'm going to shut up now but I could keep dumping for ages. In case it's not obvious, I'm kind of a book hoarder. 

A local math circle might be interesting if you can find one. You'd probably have to find an out of level one. Long-distance mathematical penpals might also be interesting. 

From where you are, you might also be able to find a local math professor or graduate student who would be interested in weekly tutoring sessions, with the idea that they'd supplement between -- even if you can't afford it, you might be able to snag someone who's willing to do it just because it's a thrill to have highly talented students who like math. You could call a local university's math department and ask. 

When you do decide to return to proofs, I'd look for something where you can get an instructor's solutions manual. One that's now open-source would be a good choice -- https://aimath.org/textbooks/approved-textbooks/ has several textbooks that were originally published but are now out of print and copyright has reverted -- and you might well be able to get an ISM from the author by explaining your situation. 

 

But with all that I've said above, I don't think it's going to do them any harm to take some time *off* math. I still think that I'd make sure that there were interesting math books around. Again, you might contact a local university and ask if any of their professors have old books floating around that they'd recommend. I picked up some of my most interesting supplemental reading books from a professor who was retiring and "get this out of here". 

[RenaInTexas]

They are at a level where they could likely teach themselves from most math books. 

Some ideas would be: operations research analysis, abstract algebra (this could be awesome, I loved it!), game theory, numerical analysis.

They could also venture into some areas where higher levels of math are used like: aerospace engineering. control engineering, learn Matlab.

Another idea could be to subscribe to a math journal (like AMS) and have them read from there and maybe take a deeper dive into an article that grabs their interest. Older issues are free on the website. (Another journal)

The challenge for them is to learn from the text and similar resources without help from mom. The challenge for you is to let them learn from those resources and not you. You take the perspective that it is more so about learning to self-learn than about learning the math/content.

BTW, I feel the exact same way about AOPS, but I never dared to say that here bc so many here adore it. I keep looking at it for my own kids and all I see is what your kids see.

Edited October 29, 2018 by RenaInTexas

[SeaConquest]

I'm no path person, but, as I recall, Quark's son read a lot of the Dover math books.

[Gil]

poof

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[Gil]

*poof*

Edited December 1, 2018 by Gil

[Gil]

*poof*

Edited December 1, 2018 by Gil

[Gil]

*poof*

Edited December 1, 2018 by Gil

[Gil]

*poof*

Edited December 1, 2018 by Gil
privacy

[Slache]

For later: https://www.amazon.com/dp/0321645855/ref=cm_sw_r_pi_awdm_LrK3vb19M7G19

What about alcumus for now?

[SoCal_Bear]

Would your boys enjoy some of the MOOC courses that are out there? LIke the MIT courses, Coursera or Edex

Edited November 1, 2018 by calbear

[Gil]

*poof*

 

Edited December 1, 2018 by Gil

[Gil]

*poof*

Edited December 1, 2018 by Gil

[Dmmetler]

We have the LOF college books. DD hasn’t done them yet except for Statistics (she’s basically redoing her math at the college to check high school and college boxes, and biologists/cognitive scientists simply don’t need some of those math classes), but DH (pure mathematics undergrad and grad degrees, although he works as a software engineer) says he wishes he’d had them as an introduction before diving into the topics-because books at that level do tend to be dry. 

[4KookieKids]

1 hour ago, dmmetler said:

We have the LOF college books. DD hasn’t done them yet except for Statistics (she’s basically redoing her math at the college to check high school and college boxes, and biologists/cognitive scientists simply don’t need some of those math classes), but DH (pure mathematics undergrad and grad degrees, although he works as a software engineer) says he wishes he’d had them as an introduction before diving into the topics-because books at that level do tend to be dry. 

 

Not to derail, but can you  tell me anything about these LoF books? My oldest was bored to tears by LoF when he was 6-7, so we quit, but we didn’t have the high school or college books. How quickly do they get more interesting?

[daijobu]

22 hours ago, calbear said:

Would your boys enjoy some of the MOOC courses that are out there? LIke the MIT courses, Coursera or Edex

 

I agree with this.  Also Great Courses offers a class on Discrete Math that's taught by Arthur Benjamin from Harvey Mudd.  He has an excellent explanation of RSA crytography, that doesn't skip over the math, but is still very accessible.  Also the videos by 3Blue 1Brown are eye opening.

[kiana]

10 hours ago, 4KookieKids said:

 

Not to derail, but can you  tell me anything about these LoF books? My oldest was bored to tears by LoF when he was 6-7, so we quit, but we didn’t have the high school or college books. How quickly do they get more interesting?

 

One of my adult friends did Fred trig, loved it, did Fred calc, hated it. He went to Stewart and did better with that. 

[Dmmetler]

In general, I think Fred is a “love it or hate it” kind of thing. I do think the high school and college level books are better than the elementary ones. DD is a “loves Fred” kind of kid, and tends to work through the books before doing another math class in the same topic (AoPS until she started college math)-but I can’t say she’s chosen to work through anything beyond what she needs for fun. 

[mumto2]

12 hours ago, 4KookieKids said:

 

Not to derail, but can you  tell me anything about these LoF books? My oldest was bored to tears by LoF when he was 6-7, so we quit, but we didn’t have the high school or college books. How quickly do they get more interesting?

The first one my kids had was geometry but they went back and did from fractions up for the story.  As my daughter put it after her run through the Calculus book,  she will never have any fears about Calculus again but definitely needs more to complete the typical course.  I think the easy introduction is the benefit. 

I don’t think the elementary ones really show the quirky Fred at his best...I thought they were rather blah when I read part of one at a friend’s.  For the most part they are an introduction to the harder math but Trig stood on it’s own just fine.

Btw, I think there are samples on the publisher’s website. 

[Gil]

*poof*

Edited December 1, 2018 by Gil
privacy

[4KookieKids]

Have they already taken a modern algebra course? If not, I find many textbooks are extremely readable, and the content is just plain fun. I can reach out to my math peeps is you want, and ask for recommendations for the most readable ones they’ve seen? (I teach math at a large uni and have lots of friends from grad school also teaching at universities.)

[mumto2]

1 hour ago, Gil said:

So, The Boys are not the least bit interested in my perfectionistic belly-aching and have informed me that we **will** have math class next year, but are very open to the idea of a "different" style of math class. So I am looking for suggestions for some good "dabbling" math books/series written between a highschool or university sophomore level.

I'm actually pretty intrigued by the university level Life of Fred books. I think that Buddy could go either hate/love with them. He has a ridiculous sense of humor, but is 100% against anything that is  "babyish" and finds "gimmicky" unappealing. But he has an absurd sense of humor (his Nanowrimo story is about an immortal goat who is the worlds greatest mathematician) so...maybe? I think that Pal will be entertained (possibly distracted) by the goofiness of the layout and story, but he'd at least finish the book.

From reading the samples of Calculus, Real Analysis and Linear Algebra, I know those books would make me nuts. I'm firmly in the hate it camp--but I think I'm going to get them one anyway. We've done a lot of math over the last 7 years and I'm kind of at a loss of where to look next. Next year, our math class will be different in at least the following ways:.

1) Won't require a lot of prep for the teacher (ie Me)
2) Not focused on "harder" math (ie going to the next level in a sequence)
3) Not assigning every problem in the book, but it would be nice if it had some problems for us to work on.
4) No going willy nilly down rabbit trails. After 6+ years, I can say that 'willy nilly' just doesn't work for us.
5) 2-1. They're eager to do weekly presentations on mathematics concepts. So each of them will have one math-centric speech/presentation/demonstration each month
6) Organized around units, we'll be spending 2-6 weeks with a book/source/topic?
7) Minimal homework for them

I really want dabble-ready stuff that we can get through or set aside after 2-6 weeks. 

We've worked off and on Dovers Challenging Problems in Algebra/Geometry, and Competition Math for Middle School there isn't enough left in either of those books to keep us for a year. So I'm thinking the Five Days LOF might be an interesting addition to the pile for 2019.

Any thing else you'll can think of? It needs to be print or readily printable, but print books are preferred by a long shot.

 

 

?. Considering Fred’s pet Llama destroys a football field at the start of Geometry this could be a good match.  All sorts of really absurd things happen in those books.

[daijobu]

How about Gentle Introduction to the AIME by Scott Annin?  Or poke around the MAA bookstore and see what looks interesting.  

[kiana]

Dover, Flegg's From Geometry to Topology. I used this as an adjunct to a topology class that I was teaching in an effort to try to make these complicated concepts more intuitive. The author was intending it as a prologue to a university course (in the UK, so they would already have passed their A levels) or a supplement for interested students in the sixth form (11th/12th grade, taking A levels). No real chapter exercises, some exercises at the end of the book.

More Dover -- the book Sequences, Combinations, Limits, by Gelfand (not I.M. Gelfand, different one) et al.22

Many books from the Anneli Lax New Mathematical Library -- some specific titles could include Coxeter's Geometry Revisited (you can find this online for a preview if you look in the right places), Niven's Mathematics of Choice, Beckenbach's Introduction to Inequalities, and there are more.

If the book's inexpensive, don't be afraid to work a chapter or two and then say "nah, doesn't suit us at the moment". 

[Gil]

9 hours ago, 4KookieKids said:

 Have they already taken a modern algebra course? If not, I find many textbooks are extremely readable, and the content is just plain fun. I can reach out to my math peeps is you want, and ask for recommendations for the most readable ones they’ve seen? (I teach math at a large uni and have lots of friends from grad school also teaching at universities.)

Hmmm...do the students find the textbooks extremely readable? After awhile, many times college professors/teachers forget what it's like to have "first time, learners" eyes when reading some thing they consider "enjoyable" or "simple".

Don't get me wrong; I'm open to doing a short course (iow dabbling) in Abstract/Modern algebra, but we haven't totally mastered Proofs or Real Analysis, and  I've never taken Abstract/Modern Algebra course either I'm really hoping that doing Abstract/Modern algebra won't become one of those things that will suck me into Intensive Preparation Mode.
Next year, I really need math to be easy for me to teach well, so that I can focus my energy more in other areas. 

[4KookieKids]

3 minutes ago, Gil said:

Hmmm...do the students find the textbooks extremely readable? After awhile, many times college professors/teachers forget what it's like to have "first time, learners" eyes when reading some thing they consider "enjoyable" or "simple".

Don't get me wrong; I'm open to doing a short course (iow dabbling) in Abstract/Modern algebra, but we haven't totally mastered Proofs or Real Analysis, and  I've never taken Abstract/Modern Algebra course either I'm really hoping that doing Abstract/Modern algebra won't become one of those things that will suck me into Intensive Preparation Mode.
Next year, I really need math to be easy for me to teach well, so that I can focus my energy more in other areas. 

 

As an undergrad, I found my modern algebra text extremely engaging and readable and it was my first higher level math course and I’d never seen proofs before and didn’t do real analysis until the semester after. It’s possible I was already twisted, but I actually enjoyed reading my book before coming to class! ?

[Gil]

Alrigthy then, which Abstract/Modern Algebra texts do you and your crew most recommend?

[kiana]

This abstract algebra text was designed for students who really hadn't had a formal proofs class -- they've had linear algebra, and done the proofs there, but not much more: https://www.amazon.com/Abstract-Algebra-John-Beachy-ebook/dp/B00GUOBNFG/ref=cm_cr_arp_d_product_top?ie=UTF8

The authors also have a companion website, with supplemental problems, a lot of which have solutions here: http://www.math.niu.edu/~beachy/abstract_algebra/

*I* thought Fraleigh was very good for an undergraduate introduction, and having taught a one-semester abstract algebra class out of it several times, I find that it has really helped my *own* complete/thorough understanding of the material as well. As you know from your preparation, there is a huge difference between having a decent understanding of a subject as a mathematics student and having a decent understanding as the instructor. It may be too advanced for what you are looking for, but I mention it. There are some really interesting sections in it -- Chapter 12 (he has "chapters" where many would have "sections" in particular has some very interesting stuff on plane isometries. If you (or anyone else who's reading this thread) go for this one and want some answers checked, pm me -- I've graded many of the homework problems before and kept my notes when I moved. 

I know one of the Allendorfer and Oakley books from the 1960s -- Fundamentals of Freshman Mathematics, maybe, or Principles of Mathematics -- had a couple of chapters on it. This was during the "New Math" era when abstraction was heavily pushed. I inherited a large collection of books, including these, and was skimming them and very surprised to see that included. Unfortunately, some of my more esoteric mathematics books, including these, are still boxed up after a recent move. If I can figure out what box it was in (and remember to update) I'll share it here. These are some very good books for future mathematicians and used copies are usually available on amazon. 

Another interesting book for a first exposure would be Carter's Visual Group Theory. This one works very hard at building intuition for this subject that is often presented so abstractly that not only can you not see the forest for the trees, but you cannot even see the trees for the leaves. You can preview the first couple of chapters here: http://www.mathcs.emory.edu/~dzb/teaching/421Fall2014/VGT-Ch-1-2.pdf

While I'm thinking about it, another book that I should have added to my earlier post would be Weissman's Illustrated Number Theory. Again, there are a tremendous number of worked examples, and number theory is something that is very amenable to dabbling.

I should also have mentioned David Burton's Elementary Number theory, which I used myself for self-study and found incredibly approachable. I had (at that point) had calc 1-3, linear, diffeq, and was taking discrete math. 

ETA: I am now thoroughly distracted from the test I was supposed to be writing because this is much more interesting ?

I just stumbled across this book -- https://www.amazon.com/Ingenuity-Mathematics-Anneli-Mathematical-Library/dp/0883856239/ref=wl_mb_wl_huc_mrai_1_dp?ie=UTF8&pd_rd_i=0883856239&pd_rd_r=HWXQTYQE9Z3QV2WCZJXP&pd_rd_w=vusuY&pd_rd_wg=1D9Jc

I have absolutely no experience with it, but the reviews are great, the price is not expensive, and it looks like it would be a near-exact fit for "dabbling". 

Edited November 10, 2018 by kiana

[4KookieKids]

3 hours ago, Gil said:

Alrigthy then, which Abstract/Modern Algebra texts do you and your crew most recommend?

 

I have a fb message for my friends out and will update when I hear back. In the meantime, this is the book I used as an undergrad that I thought was super fun:

https://www.amazon.com/Abstract-Algebra-First-Undergraduate-Course/dp/157766082X

i no longer have access to it so can’t peruse it to re-evaluate the opinion of my younger self... lol. So if you could find a sample somewhere, you might run it by them. In particular, I didn’t need it to stand alone at the time, so it might have been a pleasure to read, but insufficient for self-teaching anything.

Another popular choice is this one (that my current university uses- I find it very readable, but I may be out of touch ? )

https://www.valorebooks.com/textbooks/abstract-algebra-an-introduction-3rd-edition-3rd-edition/9781111569624?gclid=Cj0KCQiAoJrfBRC0ARIsANqkS_7Sg9k9AtPHGGrTFDnorh1uOztY81eAA5QJMMNqkYNFx0crNKWQIhAaAvUrEALw_wcB&gclsrc=aw.ds

Edited November 10, 2018 by 4KookieKids

[Gil]

On ‎10‎/‎30‎/‎2018 at 11:21 AM, OneThoughtMayHideAnother said:

Gil, this is so inspiring. Do you happen to have any notes or blog posts detailing your boys' math journey? I'd love to learn from your experience. Very curious as to when they started, what curricula/books you used, what material got covered when (e.g., 3rd and 4th grade in one year, etc), daily math routine, participation in any math enrichment/competitions outside the home, etc. You will now have so much time to cover other exciting subjects before the boys leave home! Great work!

Sorry, I didn't mean to blow you off. Would you rather know what I did, or what I'd do if I had a do-over?

General guidelines to use when accelerating young NT kids
0) Know your child(ren) above all else. Do what it takes to inspire your kids to feel confident, engaged and interested by mathematics.
1) Define your target. Devise a way to hit it.
2) Be the boss and own that role. You, not the kids, are in charge of programs goals and objectives.
3) Prioritize building the kids confidence and competency in the basics, over adding in rigor or challenge prematurely.
4) "Learning Styles" are pseudo-science crock that commercial educators came up with to sell products. So pick or create the resources that can get you down the path that you want to travel, but don't waste a ton of time and energy obsessing or trying to cater to a perceived learning styles in little kids. Little kids just learn. "Hands on" kids don't ignore the parts of the world that they can't touch, (or they wouldn't know how to speak) "Auditory" kids don't remain baffled about things that they can only see or they'd be stymied by a game of hide and seek.
5) The teacher has to put in the work. If you aren't working 3x harder than your kid, you're asking too much of the kids--you're likely going to burn them out.

--Note:I'm 100% against programs that are "independent" for the kids and "easy" for the parent/teacher. If your kid is 12 or under, they need your supervision, guidance and attention. Period.
6) Only use intelligently designed drills, that are scheduled regularly and completed in a productively.
7) Be present and proactive in your kids learning.
8) If you have to choose between challenging young kids, or building their foundation--chose the foundation.
9) Do not sacrifice your kids sense of accomplishment or confidence in mathematics on the alter of rigor. It is easy to challenge kids on a topic that they are rock solid and super confident with. At that point, the challenging problems enhance their understanding, not call it into question and make them doubt.
 

[Gil]

3 hours ago, kiana said:

I just stumbled across this book -- https://www.amazon.com/Ingenuity-Mathematics-Anneli-Mathematical-Library/dp/0883856239/ref=wl_mb_wl_huc_mrai_1_dp?ie=UTF8&pd_rd_i=0883856239&pd_rd_r=HWXQTYQE9Z3QV2WCZJXP&pd_rd_w=vusuY&pd_rd_wg=1D9Jc

I have absolutely no experience with it, but the reviews are great, the price is not expensive, and it looks like it would be a near-exact fit for "dabbling". 

It does look like a good fit. Its on the short-list.

[Gil]

3 hours ago, kiana said:

...Another interesting book for a first exposure would be Carter's Visual Group Theory. This one works very hard at building intuition for this subject that is often presented so abstractly that not only can you not see the forest for the trees, but you cannot even see the trees for the leaves. You can preview the first couple of chapters here: http://www.mathcs.emory.edu/~dzb/teaching/421Fall2014/VGT-Ch-1-2.pdf

While I'm thinking about it, another book that I should have added to my earlier post would be Weissman's Illustrated Number Theory. Again, there are a tremendous number of worked examples, and number theory is something that is very amenable to dabbling.

Wow, Kiana these both look really fantastic. If I'm not careful you're going to bankrupt me!

I've been looking at all of the books you recommended and am refiguring the budget >_<. I'm over here wondering if they can do without the Spanish tutor for a couple of weeks...

I kept saying that I didn't want anything for the holidays, but I'll have to change that and tell people that I want an Amazon Giftcard. ?

[kiana]

On 11/10/2018 at 4:07 PM, Gil said:

Wow, Kiana these both look really fantastic. If I'm not careful you're going to bankrupt me!

I've been looking at all of the books you recommended and am refiguring the budget >_<. I'm over here wondering if they can do without the Spanish tutor for a couple of weeks...

I kept saying that I didn't want anything for the holidays, but I'll have to change that and tell people that I want an Amazon Giftcard. ?

 

If I'm not careful I bankrupt myself too. 

 

My amazon wish list is hundreds of items and my "potential math textbooks" is longer. 

[Gil]

Our tentative Booklist for next year includes

• Visual Group Theory
• An Illustrated Theory of Numbers
• A Gentle Introduction to the American Invitational Mathematics Exam
• Life of Fred: Five Days of Upper Division Math
• Random back issues of College Mathematics Journal and MAA Focus, as they seem most accessible and suitable to our purposes and can be bought off eBay

I'd been starting to feel stuck between the rock of rehashing stuff we've seen and the hardplace of stuff that's way over our heads, so I'm excited that these books can breath some new life into our math-time. I like that these books are playful, visually appealing and seem easy to read/follow. Its expensive, but worth it to have books that draw them in and hold their interest.

[nixpix5]

On 10/27/2018 at 1:17 PM, regentrude said:

I am completely puzzled by this comment. Physics is everywhere in everybody's everyday life. How a ball flies, how a car drives around a curve, how it stops, how the Earth revolves around the sun, ,why there are seasons and tides,  how your computer and your stereo work, how your cells let the sodium and potassium ions in and out, how your brain tells your foot to move, how your eye sees, how a telescope works... how is that "niche" and doesn't reach everything? Every object, every organism, every cell and cell organelle, every planet and every elementary particle is subject to the laws of physics.

ETA: I would not stop math. I would seek out resources to learn math off the beaten path. Have you completed AoPS' number theory and counting&probability? Great topics, books written to the student so that no outside instructor is necessary.

This. I was a little floored by the statement too. Every science discipline is basically just a spinoff indepth topic of physics. Maybe if you think of physics as the programming code of the universe you could learn to love it more 😋