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39 points

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6th Feb 2018

As someone who has studied dynamical systems for years, I'm pleased to see so many redditors getting interested in them through the double pendulum system. If you're a student and want to learn more, take a course in dynamical systems. If you're not a student, consider reading this book, which is my favorite math book of all time, and I'm far from alone in that sentiment.

27 points

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15th Dec 2018

I just went through this process very recently so I can at least tell you what the process is like.

First you apply for a position on Google's career page. If your CV is up to snuff a recruiter will contact you shortly and give you a brief phone screen.

Second they have you sit down and do two more interviews via hangouts. One of them will be coding and one will be talking about your recent research. I got the idea that the primary goal was to verify that you did indeed meaningfully contribute to the research. They ask fairly in-depth technical questions, things that anyone other than the primary author wouldn't know.

Third they invite you to do an on site in Mountain View. There you're expected to give a talk about your research (45 min + 15 for questions), followed by a full day of interviews. Those interviews will be some combination of coding and research interviews. The research interviews will be other research engineers asking you about your previous research history. I was quite shocked at how thorough they were. They asked questions about stuff I did in undergrad, and even about one paper that I ended up scrapping and was never published. I still have no idea how they even got a hold of a draft.

All of the coding interviews were fairly straightforward if you know your stuff. None of them were the sort of tricky nonsense (like competition coding questions) some companies give. They were things like implementing simple ML algorithms (e.g. logistic regression), basic algorithms (e.g. depth-first search), or simple/baseline models from my subfield.

As far as preparing goes, I got a copy of this book. It was kind of useful for practice but way trickier than anything Google threw at me. In my opinion the best preparation you can do is to know your own project/research history inside out, and be ready to explain one recent work in-depth on a white board in ~15 minutes.

2 points

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5th Dec 2020

It will depend on your level and the area. The best beginner book IMO is Nonlinear Dynamics and Chaos by Strogatz

1 point

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17th Oct 2022

I found it. It's from the book, *The Drunkard's Walk*. It's a 269-game series. Here's a link to the book. It's one of the best books I've ever read. Definitely a big recommend, especially to fellow stats nerds.

1 point

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22nd Dec 2020

Dynamical systems theory is a subset of the study of differential equations.

If you want to understand dynamics, you need to analyze the differential equations involved. My suggestion is to look into bifurcation theory and ODE methods since they can be extended to the study of PDEs. Dynamical systems isn't so much about solving the specific partial differential equations as it is about using them to understand the behavior of said system.

If you want an actual primer to the subject, the Strogatz book Nonlinear Dynamics and Chaos. Link is a very good way to begin understanding it.

But there isn't a good way to get a decent understanding of dynamical systems without dealing with differential equations because the study of dynamics is the study of differential equations.

1 point

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4th Dec 2020

I felt kind of the same way until I took a dynamical systems class. Sometimes you just need to find that area that you actually enjoy. I really didn't get the abstract part as easily, but applications peaked my interest just by virtue of being able to see the results of what all the abstract stuff could do.

Have you decided where you want to focus yet and where you want to lean into?

I had a weird path in school, so I ended up taking physics at the same time as I was doing complex analysis, and I remember immediately seeing the applications of what we were doing when we entered electromagnetism in physics. Its one of the main reasons I chose to stay on the math road rather than changing over to CS.

My suggestion is to branch out a bit and find some stuff you really like in math. Personally I found group/ring/field theory super boring, but analysis was really interesting. You should try to find a niche that sparks your interest or makes you interested in what you could do with math.

For some suggestions on interesting applied math topics (IMO of course) are numerical analysis and dynamical systems. Dynamics absolutely blew my mind so much that it solidified my decision to go to grad school and learn more about it.

Edit: if you want to see a really interesting book on all of the applications for diffeq, check out nonlinear dynamics and chaos by Strogatz

1 point

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23rd Jul 2019

On Amazon it got good reviews, although I cannot understand why?

The code is literally UNREADABLE, the above code is the first code in Chapter 6, Strings

​

Elements of Programming Interviews Python

https://www.amazon.com/Elements-Programming-Interviews-Python-Insiders/dp/1537713949

1 point

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17th Sep 2020

I don't know any Youtube channels that specifically prep for Python Interviews. However, EPI in Python is probably the only book you'll need to prep for interviewing in Python.

1 point

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22nd Aug 2020

Well... A lot of areas, actually. The main branch of mathematics that studies CA is called Complex/Dynamic systems, it focuses on the idea of interactions between certain systems and that's what gives us a framework around "rules of CA", I recommend the resources of the Sant Fe Institute along with this book there are some other math areas important to the subject, the key one is just discrete math, so you can get along the idea of recurrence, but it seems like you have some good programming background so you've probably taken a course on the subject already.

1 point

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17th Dec 2018

3.4 - Create a stack class (with all normal stack operations). Create a queue class using two stacks. You can than implement the enqueue / dequeue operations using the "in-stack" and "out-stack" like in the book.

It can be alittle confusing to go from the java solutions to python solutions, but just remember that python is not as verbose as java. And like /u/electricave21 said, check the CTCI repo for python solutions.

I also personally found Elements of programming Interviews in Python to be very helpful.

1 point

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2nd Sep 2018

Hi there, $5 for Calculus for biology and medicine 4th edition

1 point

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25th Aug 2018

Elements of Programming Interviews in Python: The Insiders' Guide for people who are working towards getting their first python job. The book contains common interview programming questions with the solutions in python. Great way to learn the basics of algorithms and data structures needed for a technical interview. 456 pages ($21.56)

1 point

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7th Jun 2018

I just picked up this book:

Sciencia: Mathematics, Physics, Chemistry, Biology, and Astronomy for All (Wooden Books) https://www.amazon.com/dp/0802778992/ref=cm_sw_r_cp_apa_i_S5hgBbHC27QE0

It has a very broad overview of the world and those subjects. It is a summary of 6 different books. They are:

Mathematical Proofs Math and Physics formulas Chemistry Evolution and how life evolved The Human Body The Cosmos

I'm just barely starting it, but it has a lot of good information that starts from basic concepts and goes into more advanced topics. For example, it contains the proof for why a triangle has 180 degrees early on but later, in the physics and math section, goes into quantum physics and electromagnetism to name a couple.

Good luck :)

1 point

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11th Dec 2017

One thing is, after a BSc, on may doesn't have a good picture what "modern physics" is alike. Old fields like classical mechanics is so structered, and e.g. quantum mechanics seems arbitrary. At least I had the feeling back then. That's because those older fields had more time to mature, and there is more structure to appreciate from the outset. It turns out that usually one has to learn a bit more to understand why "modern physics" is cool. E.g. quantum mechanics allows for kick-ass new materials with topological phenomena and quantum computing/information processing.

Nonlinear dynamics and Chaos is really cool. It has lots of structure from classical mechanics. Have a look at this book

Astrophysics has also overlap with classical mechanics, e.g. for my MSc thesis I worked with Hamiltons equations with a general relativity metric.

1 point

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5th Nov 2015

Subcategory: dynamical systems.

For undergrad level: Strogatz Nonlinear Dynamics and Chaos

For graduate level: Perko Differential Equations and Dynamical Systems

1 point

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27th Apr 2015

Some very good points.

Actually, R2 is really bad for model comparison. Many authoritative sources recommend theoretical-based measures such as AIC, AICc, BIC.

1 point

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16th Oct 2012

It is really good at giving clear and concise answers to many questions about the universe, math, and chemistry without a need for any prior knowledge in any of these fields. The book uses simple language, along with clear diagrams and illustrations of the concepts to quickly paint a broad understanding of each topic.

1 point

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22nd May 2012

For notions like this I can only recommend a book. The Drunkard's Walk: How Randomness Rules Our Lives

1 point

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23rd Apr 2012

It's cool that you're interested in complex systems, but your post is a bit vague. I liked Nonlinear Dynamics and Chaos (Strogatz). It is a very easy/friendly intro to the field. Another good book, depending on what you're wanting to do, might be Daniel Gillespie's book on markov processes. In general, you basically need to read some papers, find a type of problem/approach that interests you and then fill in the blanks with supplementary material. Most of what you need to know is in a journal somewhere. Google that shit. If you want to code stuff, learn python & C.

1 point

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1st Oct 2012

Yep, that's the strategy. A detailed proof would look like:

Let q=max(a,c) and r=min(b,d) and consider the interval (q,r). If a number u is in (q,r) then u>q so that u>a and u>c. Also u<r so u<b and u<d. Therefore we can conclude that u is in (a,b) and (c,d). Finally, since u was chosen arbitrarily from (q,r), we may conclude that __any__ point in (q,r) is in both (a,b) and (c,d). Thus, (q,r) is a subset of their intersection.

I've never read it, but I've heard from many that "How to prove it" is a good intro to proof based math. Don't worry so much about "fundamentals" in the sense of mathematical facts that you may have forgotten. Generally, all of the facts and definitions you need to know will be reviewed at the beginning of an undergrad proof-based book or course.

If you think you might be interested in applied math, check out this book by Strogatz. It's a great intro to thinking like an applied mathematician, which is more about intuition and visualization than proofs and logic.

1 point

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19th Dec 2011

I would recommend checking out later sections of this book http://www.amazon.com/Mathematical-Biology-Introduction-Interdisciplinary-Mathematics/dp/0387952233 (I can PM you a pdf if you want it). It goes into protein-protein bonding and protein-small molecule reactions in glorious mathematical sparseness, succinctly covers molecular biology/bioinformatic screens, and of course covers everyone's favorite intro PDE- the predator prey model; even after taking upper level undergraduate biochem/molecular biology courses seeing it all put so succinctly was a real treasure. Some of the math is relatively advanced for a developmental math course, but given that all of your biology/chemistry majors should have covered this material before (sans math in most cases) it shouldn't be too hard for them to jump into.

1 point

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31st Dec 2011

This is mostly what I wanted to explore after reading about him in The Drunkard's Walk. I'm very interested in other cases like his. It fascinates me.

1 point

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11th Aug 2010

I really enjoyed The Selfish Gene, I always wanted to read The Extended Phenotype, but as a layman I didn't get past the lengthy introduction let alone get to the meat.

My favourite book by Dawkins is The Ancestor's Tale, it walks along the tree of life starting at humans back to the first self replicating molecules, telling an interesting tale about a type of life at each branch.

1 point

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9th Mar 2010

Strogatz writes in a very easy to understand manner. For those interested in chaos theory and nonlinear dynamics, this is the book to read.

1 point

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6th Sep 2010

You should read this book: The Drunkard's Walk: How Randomness Rules Our Lives, all your questions about randomness and probability of events will be answered.

Here, read one of the comments taken from the Amazon site. >I just love books like this - especially when they're as well-written as this one. The author, a physicist, proceeds to show the reader how randomness plays a much greater role in everyday life than one might think. As he discusses the basics of probability and statistics, he provides wonderful illustrations from fields as wide-ranging as sports, medicine, psychology, the stock market, etc., etc. He does an excellent job in driving home the fact that the true probability of events is not intuitive. Perhaps because of this anti-intuitiveness, I had to read a few paragraphs more than once to allow the point being made to sink in. One enigma that is particularly well explained is the Monty Hall (Let's Make a Deal) problem. The writing style is clear, accessible, very friendly, quite authoritative, engaging and often very witty. This book can be enjoyed by absolutely everyone, but I suspect that math and science buffs will savor it the most. By the way, the math-phobic need not fear: the book does not contain a single mathematical formula.

1 point

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12th Dec 2010

Oh, I agree about the whole "above average" thing. It's pretty ridiculous but, then again, people are horrible with stats-related stuff in general. You might like this one book that has a lot of great anecdotes and data on the subject. And as for

>my opinion lacks subjectivity

you're closer saying "lacks objectivity" or "is subjective" (got 'em switched around, I think) although, really, it's a different story. I mean, if you never drove, you just don't necessarily know the experiences related to how you can deal with the road. However, I do think you are more than justified to protest bad driving habits because drivers can very much forget about how non-drivers perceive these things. In general, though, I think that people should be arrested/ticketed for dangerous/reckless driving for whatever reason (to a point), and "oops, I dropped my cigarette and swerved" shouldn't necessarily be held to any less accountability than "oh, I've had a few..."

1 point

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29th Jun 2010

This seems pulled straight from a book the was recently published.

http://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0375424040

The only difference is that it is about Girls and the problem is far better explained.

1 point

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14th May 2010

1 point

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16th Mar 2010

Have you read this book??

I am reading it at the moment, and it is a fantastic read, with a lot of great real life examples. Someone such as yourself is probably at, or above, this level, but I recommend it for others who are interested in the topic!