Reddit reviews All the Mathematics You Missed
We found 23 Reddit comments about All the Mathematics You Missed. Here are the top ones, ranked by their Reddit score.
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Reddit reviews All the Mathematics You MissedWe found 23 Reddit comments about All the Mathematics You Missed. Here are the top ones, ranked by their Reddit score.
Think about basic high school math. You might have forgotten a few very specific ideas to solve a few very specific problems, but it's likely you remember almost all of it.
Why? Because you used it exhaustively in your basic undergrad math courses. Setting a derivative = 0 often demanded you factor, even if your directions never specifically said "find all solutions to this equation."
So, maybe you forgot a specific application of something like finding the principal value given blah blah compounded continuously, but you certainly know how to rearrange equations to solve for a variable.
Using something was practice, and so it was ingrained into your head (plus, after years of doing it, it's simple and downright monotonous).
But what about now? Were you extensively using Weierstrass's M-test on series in later classes? If you say yes, I won't believe you. Can you still find the integral of an obnoxious complex-valued function using residue theorems? Did you use these extensively in other classes? Doubtful, but possible.
This is the problem you are facing. I STRONGLY DOUBT you've been underexposed, but I HIGHLY AGREE with the possibility that you've forgotten.
So here's the important question: CAN you go back and relearn things? You say "progress is slow," but this is not a real answer to my question. Given one hour each day, can you, in 3 days, Mon/Wed/Fri, reteach yourself to determine if a metric space is compact? If you say Yes, then you are in a great position! There are many who sit through the class in one week and still have no clue! If you say No, then you're not necessarily in a BAD position (though you might be), you're just possibly in NO position.
So, here's the idea: you can't get good at upper level math (which will be considered lower level MATH math when you're going through grad school) by simply figuring it out. You got good at lower level math through practice; this is how you will get good at upper level math.
So what if progress is "slow"? Speed is subjective, but it's far more important that you CAN solve abstract problems rather than being able to blast through them--speed will develop later, and I know many PhD students at great schools who don't always remember what the subgroups of some strange group are or even how to find them.
So, let's answer, now, your REAL question: are you in for a rude awakening?
Yes, you are. But not for the reason you suspect. When you are in grad school, your faculty will (or it BETTER) have higher expectations of what you know vs. what you can do, and they're more concerned with what you can do than they are with what you know (forget something? Look it up. Forget how to do something? Looking it up may not help you...).
The fact that you are making ANY progress at ALL is enough to show that you are capable of doing things, even if you don't know things.
But are you in for a rude awakening because things are going to be hard because you've forgotten so much knowledge and thus you might have made a mistake because you'll never get up to speed? No. Most of my graduate level courses redefined things defined for me back as an undergrad, since at that level it gets difficult to figure out what students know and what they don't know based on where they came from.
But let's not build false hope and try and stay grounded in reality by this--
Check out this book: http://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
Tinker through it and, when you're done, retake the MGRE. If all goes well, you're fine. If not, then you may very well not be. Don't rely entirely on that book to fill in gaps: use it for the TOPICS it presents, read through it, and when you're confused go find ANOTHER source relevant to the current chapter to fill in the gap.
But don't be crazy: I specifically never went through chapters 5,6,7,8,12,13,15,16 until I was in grad school. So, rather, figure out what you did as an undergrad, and go through THOSE relevant chapters in this book to get you up to speed with the ideas, and maybe dabble in some other chapters as time allows.
Here's a great reference that I didn't know about before grad school: "All the Mathematics You Missed: But Need to Know for Graduate School" https://www.amazon.com/dp/0521797071/ref=cm_sw_r_cp_api_-Zqryb5W5PQEA
It's not for learning new subjects, rather it's useful for seeing context and figuring out where your weak points are so that you can brush up using more thorough references.
There's a nice little book, All the Mathematics You Missed: But Need to Know for Graduate School, that serves well as an answer to your question. It's pretty well-written, and lives up to the title.
In my opinion, the ideal undergraduate has had introductory courses in real analysis/advanced calculus, algebra, general topology, differential geometry of curves and surfaces, complex analysis, and combinatorics. Furthermore, more than one semester of linear algebra would be preferred.
Proceeding with knowledge gaps is something everyone has to do. In your case, you're going to have to improvise a lot. What I tend to do is put a black box on any confusing detail and write it off as
"this blackbox let's me do X." If a definition is confusing for me, I replace the definition with an example that I understand and leave it be. (Some definitions have this sort of infinite regression to it; to understand this definition, you need to understand these other 3 definitions, which requires you to understand these 9 definitions and so on.)
Normally people have to take classes and pass an exam so you have at least 1 year to build that knowledge.
I don't recommend trying to learn what took others years to learn in 1 month, that's just unrealistic. Talk to your advisor; a lot of times you don't need to know the subject 100%, just some parts of it.
For analysis, you might not need to know everything about it, just maybe what a Hilbert space is and some standard results. For complex, honestly I think that class was more to teach people how to do analysis (the proofs are very elegant and it really give you experience on how one ought to go about proving something in classical analysis), as far as results goes, I only know the residue theorem and Riemann mapping theorem. For algebra, I guess I know what all the structures are... but don't remember much else.
Oh, there's this book that supposedly give a good outline on math you need to know.
I didn't read your other post. But one suggestion is that if you're having trouble in a grad level class, figure out what undergrad prereq you're missing. For example I was weak in multivariable calculus so I had a heck of a time in differential geometry. The problem wasn't with the grad level material, it was my lack of mastery of the corresponding undergrad material.
So figure out what you missed in your undergrad years and work on that.
There's a book I wish had been available when I was in grad school.
All the Mathematics You Missed: But Need to Know for Graduate School
Also do you join study groups with other students? That's a great way to learn.
I've already made a comment but I just remembered that this book exists:
https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
You might find it helpful
This book in conjunction with this book should keep you busy.
Consider using Anki for stuff you want to review periodically and already understand.
http://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
Munkres is a great resource to learn topology if you want to actually learn the material and as for complex I don't have a good suggestion for it, but since you're trying to study for the GRE I would suggest checking out All the Mathematics You Missed but Need to Know For Graduate School by Thomas Garrity. The link I added leads to the amazon page where you can buy it for pretty cheap. It's a great book that contains the two subjects that you want to study and many more topics. I myself am using it to study for the GRE and am finding it very helpful in learning the subjects I haven't touched.
http://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
Agreed with these recommendations. I'd also suggest All the Mathematics You missed But Need for Graduate School as a useful supplement.
Consider getting and working through Thomas Garrity's wonderful All the Mathematics You Missed But Need to Know for Graduate School. It's quite dense, but the goal is to help you develop intuition for all of the fields you listed and more. You won't really be able to learn a semester's worth of knowledge over the summer, but if you come into your coursework in mathematics with some intuition for what you're learning, you will have a huge leg up.
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3.) Something food related that is unusual: Food picks from my Silly Fun list! Maybe not super unusual in Japan, but here in America I doubt you'd see them often.
4.) Something on your list that is for someone other than yourself: This book off my Books wishlist of course! It's for my husband, who's a huge fan of the Elder Scrolls games. I like them, too, but I doubt I'd ever read this.
5.) A book I should read: The Invisible Gorilla, again, off my Books list. I read almost a third of this book while hidden in a book store one day. It's an absolutely fascinating study (or rather, collection of studies) about how much trust we place in our own faulty intuitions.
6.) An item that is less than a dollar, including shipping... that is not jewelry, nail polish, and or hair related: Barely, but this nautical star decal! Unfortunately, it's not on any of my lists.
7.) Something related to cats: Another from my Books wishlist! I'm pretty sure I already know my cat wants to kill me, but this book looks funny anyway.
8.) Something that is not useful, but so beautiful you must have it: Stationary, from my Silly Fun list. I have no one to write to, but I have an obsession with pretty stationary and cards and things. I'm usually too afraid to write on it, even, because nothing ever seems worthy of the pretty paper...
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11.) Something that would have a profound impact on your life and help you to achieve your current goals: This book which is, strangely, on my Semi-Practical list. I'm a Math/Physics major, but I haven't been in school in quite a while. I'm about to go back very soon, and I'm a little petrified of failing out.
12.) One of those pesky Add-On items: Red Heart yarn from my Crochet wishlist!
13.) The most expensive thing on your list. Your dream item: The PS4 from my Video Games list. I'm an avid gamer. Video games are how I relax. It's one of the few things that, no matter how crappy my day was, always manages to raise my spirits and help me forget about it all.
14.) Something bigger than a bread box: Apparently bread boxes are way bigger than I thought, so I'll go with this desk off my Semi-Practical wishlist. Surely that's big enough! XD
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Fear cuts deeper than swords!
Optics takes a fair amount of math. If you want to read something useful, I recommend:
This was an excellent primer I used the summer before grad school, it's all undergraduate level math. There's an analysis section and algebra section. https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
All The Mathematics You Missed is a good overview of topics that are good to know for graduate school. Not all of them are on the GRE, but the summaries of the GRE topics hit most of the key points.
As a first step, you should decide what your dream career is. You're considering a Master's degree - why not a PhD? Or maybe a second Bachelor's in a related field would be more appropriate? It all depends what you want to do as a career.
You might want to see this book: https://amzn.com/0521797071 - This book won't teach you everything, but it could help you get started. Then start looking into the math GRE (the math subject test - not the math part of the general GRE). Buy some prep books for that and try taking a practice GRE. See how much of that material you know.
Once you attempt a practice GRE , it should help you figure out how prepared or underprepared you are. At this point, you will probably want to sign up for some senior-level undergraduate math classes like Calc 3, Real Analysis, and ODEs. Once you can get an acceptable score on the GRE, you should apply to graduate programs.
If you're able to, I think you should consider a PhD program with a teaching assistantship. These programs offer a tuition waiver and a small stipend as payment for you teaching. Master's students often don't get any financial support. It's possible to complete a PhD program without getting into debt, and picking up a Master's along the way is optional.
Keep in mind that a graduate program might require you to take some undergraduate courses. If they don't require it, they might suggest it. You should take their advice and sign up for these classes. I had to take undergrad Real Analysis during my first semester as a graduate student, and everything worked out fine.
Good luck!
Wikipedia...
(https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071 - you can try this, but Wikipedia has more info...)
Entrepreneur Reading List
Computer Science Grad School Reading List
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All the Mathematics You Missed - Thomas Garrity
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I've been reading through this over the last few days. Seems like it might be what you're after. Does a nice overview of all the major topics covered in in a standard undergrad curriculum.
https://www.amazon.com/All-Mathematics-You-Missed-Graduate/dp/0521797071
http://web.evanchen.cc/napkin.html
and books by Ian Stewart/David Tall and Courant/Robbins What is Math,
https://press.princeton.edu/titles/10697.html
Hard to say without knowing your exact course (is it taught or research based?). Speak to your supervisor and/or current students to get an idea of what you'll be doing. If you can, read some relevant and current academic papers to get a grasp of where you have gaps in your knowledge.
I also recommend 2 general books:
There are probably better books for you depending on what you'll be doing. For example, my particular research involves multivariate analysis, so I have a variety of dedicated statistics books, including course materials from another school that teaches relevant topics.
I would suggest you find out more about the work to come (courses and schools can vary quite a lot), get one of those books and learn the maths you need as you go along.
Maybe start with a book like this and when you hit a wall, you get the relevant textbook and do exercises.
One of my undergrad profs said that "The only way to learn mathematics is to DO mathematics."