(Part 2) Top products from r/AskScienceDiscussion

I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.

If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.

Basics

I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.

Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.

From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.

This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.

Intermediate

At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.

This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.

Advanced

Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.

Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.

Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.

A great book about this subject is Understanding Molecular Modeling, by Daan Frenkel

http://www.amazon.com/Understanding-Molecular-Simulation-Second-Edition/dp/0122673514

Basically in order to understand molecular modeling you need to have a good understanding of thermodynamics (more statistical mechanics, but also classical thermodynamics).

For a good free resource on graduate level thermodynamics and molecular modeling I recommend Scott Schell's lecture notes (He is a professor at UC Santa Barbara)
Molecular Modeling Class Notes:
http://www.engr.ucsb.edu/~shell/che210d/assignments.html

Thermo and Stat Mech Class Notes:

http://www.engr.ucsb.edu/~shell/che210a/


edit to add more info:

Also- if you are doing free energy methods check out
alchemistry.org

Keep in mind that molecular modeling is a huge field with tons of methods, tons of open source and closed source software packages. More info about what specifically you want to do and what software you want to use would be helpful.
I use GROMACS to do molecular dynamics simulations, so if you have questions specifically about that I should be able to give some assistance.

One thing you might want to take a look at is an introductory historical geology textbook.

I read an older edition of this (http://www.amazon.com/Historical-Geology-Reed-Wicander/dp/1111987297) and it was generally pretty good. Very expensive there, but I'm sure a PDF is available for free with a bit of looking.

It covers the very basics of many fields (plate tectonics, Earth composition and structure, radiometric dating techniques) and then moves through major time periods of Earth's history, including dinosaurs and all sorts of other organisms.

You might find it somewhat unsatisfying in that it is covering such a vast amount of material that it can't go too in-depth proving its points every step of the way, but it does a pretty good job considering it's scope, and has lots of good photos of fossils and/or diagrams.

As a single book aimed at understanding Earth's history, I'm not sure you could do much better.

I find that science history and biography gives a good understanding of scientific methods, and when written for the lay-person, doesn't get so bogged down in technical jargon.

Here are a few of my favorites:

• A Short History of Nearly Everything - Bill Bryson
  
• Chaos: Making a New Science - James Gleick
  (Also check out his biographies of Isaac Newton and Richard Feynman)
  
• Stiff: The Curious Lives of Human Cadavers - Mary Roach
  
  And here are a few on my to read list:
  
  
• Seeing Further: The Story of Science, Discovery, and the Genius of the Royal Society - Bill Bryson
  
• Sapiens: A Brief History of Humankind - Yuval Noah Harari
  
• The Butchering Art: Joseph Lister's Quest to Transform the Grisly World of Victorian Medicine - Lindsey Fitzharris
  
• Rabid: A Cultural History of the World's Most Diabolical Virus - Bill Wasik & Monica Murphy
  
• The Wild Trees: A Story of Passion and Daring - Richard Preston
  
• The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science - Richard Holmes
  
• The Invention of Science: A New History of the Scientific Revolution - David Wootton
  
  I hope that helps.

Why not learn something about neuroscience? You'd better understand the fundamental concepts on which the brain works and how they structure consciousness. I'm not talking psychology but learning the fundamental biology of neurons and building that into an understanding of behavior and cognition.

You'd just have to read Kandel's Principles of Neural Science which is pretty much the neuroscience bible. It takes you from concepts like "Cell and Molecular Biology of the Neuron" and "Synaptic Transmission" to "The Neural Basis of Cognition" and "Language, Thought, Affect, and Learning" - the wiki lists the chapters here

edit: in fact your comfort with physics will help understand the biophysics of neurons: viewing the cell membrane as a capacitor and using circuit models of membranes with some basic V=IR stuff.

Yes, shorter generation times do result in quicker evolution (all else being equal), for the same reason that selective breeding works faster on organisms that reproduce quickly.

There are other factors that can (or are at least hypothesized to) influence how quickly a species can evolve, such as the number of offspring produced in a lifetime, DNA repair mechanisms, sexual vs asexual reproduction, and the number of chromosome sets.

A given trait may be more or less likely to evolve as well, depending on various factors.

For instance, genetic linkage can play a role in how common a particular trait becomes over time. In humans, one example would be blonde hair and blue eyes, which are genetically linked on Chromosome 15. When genes are genetically linked, it means that selection pressure for/against one trait (say, blonde hair) will inadvertently select for/against any other traits that generally appear alongside it on the same chromosome (say, blue eyes).

And, as you might imagine, genes that have a broad effect on the organism (such as the HOX genes, which control developmental processes in the body) will often evolve more slowly than other genes, because there's greater likelihood for something to go wrong in a way that kills the organism (mutations to the HOX genes can cause serious deformities). There are a lot of genes affect several traits; for example, certain pigmentation genes also relate to the inner ear (which is why some coat colors in animals, like cats and dogs, correlate with deafness; in humans, this link between coloration and deafness is called Waardenburg syndrome).

If you're interested in the rate of speciation in particular, there are numerous additional factors to consider, which relate to how two populations cease to interbreed with one another, allowing them to evolve in different directions. Contrary to popular belief, separation by long distances (as by an ocean, mountain range, etc.) is not the primary driving force behind speciation.

It's more common for speciating populations to evolve some mechanism to avoid interbreeding—e.g., different breeding times, physical changes to reproductive structures, or assortative mating. I highly recommend reading The Beak of the Finch if you'd like to learn more about it.

Sometimes external factors split population into groups that can't interbreed, leading to speciation. For example, the bacteria Wolbachia can affect the reproduction of its hosts in various ways, and it's hypothesized to promote diversity in insects.

The psychological reasons why people believe this kind of stuff are pretty easy to explain. For example see my post in this thread about confirmation bias and the look-elsewhere effect. It also might be worth mentioning that human perception is a bit of a mess; experimenting with psychedelics can be helpful in getting a sense of this, or maybe reading some Oliver Sacks. Basically there is pretty good scientific evidence that you can't always trust what you think you see. Finally, you do have a good question in there that I think is worth taking seriously: "why not?" Besides philosophical issues with mind-body dualism, I'd respond "Because there is simply no scientific evidence for it whatsoever." If there were a separate world of ghosts that could interact with our world, they would presumably be detectable through any of many extremely sensitive scientific experiments.

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-Solving

• The Art of Problem Solving - Lehoczky/Ruczyk - in two volumes, both have full solutions available separately
  
  Calculus
  
  
• Calculus - Stewart - ignore the bad reviews, it's very clear and covers all of basic calculus well - it's just the book that most intro students use and as a consequence gets a bad rap
  
  
• Calculus - Spivak - this will take your understanding of calculus to the next level
  
  
• Calculus - Apostol - there are two volumes and they are very comprehensive, albeit difficult
  
  Linear Algebra
  
  
• Linear Algebra - Lay
  
  
• Linear Algebra Done Right - Axler
  
  Differential Equations
  
  
• Elementary Differential Equations - Boyce/DePrima
  
  
• Ordinary Differential Equations - Tenenbaum
  
  Number Theory
  
  
• Number Theory - Pommersheim for a change of pace and proof skills
  
  Proof-Writing
  
  
• Transition to Higher Mathematics - Dumas/McCarthy - helps to bridge the gap between "lower" and higher math
  
  Analysis
  
  
• The Way of Analysis - Strichartz
  
• Principles of Mathematical Analysis - Rudin
  
• Real and Complex Analysis - Rudin
  
  Complex Analysis
  
  
• Complex Analysis - Ahlfors
  
  Functional Analysis
  
  
• Functional Analysis - Rudin
  
  
• Introductory Functional Analysis with Applications - Kreyszig
  
  Partial Differential Equations
  
  
• Partial Differential Equations for Scientists and Engineers - Farlow
  
  Higher-dimensional Calculus and Differential Geometry
  
  
• Calculus on Manifolds - Spivak - for a modern take on multivariable calculus
  
  
• Differential Geometry - Kreyszig
  
  Abstract Algebra
  
  
• A First Course in Abstract Algebra - Fraleigh
  
• Abtract Algebra - Dummit and Foote
  
  Geometry
  
  
• The Elements - Euclid - for culture and for understanding where math has come from, plus it's still an awesome book after all these years; don't need to go through all of it
  
• Euclidean and Non-Euclidean Geometries - Greenberg
  
  Topology
  
  
• Introduction to Topology - Mendelson
  
  
• Topology - Munkres
  
  Set Theory and Logic
  
  
• Introduction to Set Theory - Hrbacek/Jech
  
  
• Elements of Set Theory - Enderton
  
  
• Mathematical Logic - Kleene
  
  
• Set Theory and the Continuum Hypothesis - Cohen
  
  Combinatorics / Discrete Math
  
  
• Combinatorics - Cameron
  
  
• Concrete Math - Graham/Knuth/Patashnik
  
  
• Discrete Math - Biggs
  
  Graph Theory
  
  
• A First Course in Graph Theory - Chartrand/Zhang
  
  P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
  

Albert's Molecular Biology of the Cell. It is a very user friendly book on biology. It's pretty much considered the cream of the crop of biology and molecular biology textbooks. It will introduce you to basic science, as well as go as far in depth as you would prefer. Outside of that, journals such as Nature, Cell, Science. Good luck. Also amazon link, not to promote them, but to show what the book looks like.

http://www.amazon.com/Molecular-Biology-Cell-Bruce-Alberts/dp/0815341059

Demon Haunted World: Science as a Candle in the Dark - Carl Sagan

This book focuses mostly on supernatural phenomena, like ghosts, ESP, alien abductions, etc., and not the more political issues you raised above, but it's also an excellent intro to how our brains work (not like you think they do) and critical thinking about objective truths. It focuses more on the question of why people believe these things, not specifically on debunking them, and a lot of that is applicable to the issues listed above.

There is no single answer to the field guide question - you should just look for one relevant to your area. Conservative estimates put the number of insect species in the world around six million, so no single field guide is going to be able to tell you more than very common species for a specific area and maybe some family-level keys to give you a general idea.

As far as textbooks go this one is pretty decent. If you are in a university there's a good chance it's in your library, otherwise it's not super expensive 2nd hand.

Hawking's On The Shoulders of Giants

Gribbin's The Scientists

Smithsonian's Timelines of Science

There are also a ton of good historical books on almost every major milestone in physics - a few I enjoyed:

The Clockwork Universe by Edward Dolnick

Faraday, Maxwell, and the Electric Field by Nancy Forbes

E=MC2 by David Bodanis

Quantum by Manjit Kumar

The Big Bang by Simon Singh

I can't link you to any histories of biology or chemistry, sorry, those aren't my areas of knowledge.

If I may recommend a book that offers a good grounding for this:

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark-ebook/dp/B004W0I00Q/

Many theories deal with inflation. They all fall under the umbrella of "inflationary cosmology." I am not a theorist but as far as I understand "big bang inflationary cosmologies" currently receive the most attention. String theory type theories and loop quantum type theories can both incorporate inflationary effects so its certainly not limited to the "classical big bang" model I detailed.

Beyond pages such as this I would say you could get a hold of this book, Modern Cosmology By Scott Dodelson. It is a good overview of modern cosmological models at the high undergraduate level. The math it presents is targeted at physic students in their senior year of undergraduate (my words, not the author) but that doesn't mean a non-physicist can't get anything out of it.

Psychology is the social science related to human behavior.

Quantum Mechanics is the branch of physics that deals with the behavior of subatomic particles.

I'm not sure that the two subjects could be further apart.

For quantum mechanics, there are a ton of popular books on the subject. If you can ignore some of the sillier Eastern Philosophical rantings this is a pretty good introduction to quantum mechanics for someone without much education in Calculus, Linear Algebra, or classical physics.

http://www.amazon.com/Dancing-Wu-Li-Masters-Overview/dp/0060959681

Try a historical geology class.
Here's a [historical geology textbook] (http://www.amazon.com/Historical-Geology-Reed-Wicander/dp/1111987297) used for several, and a freebie historical book, although this looks like a combination of Physical and Historical more than strictly historical.

Course slides with excellent diagrams for the basic principles of how rocks are deposited.

List of Internet resources for historical geology

Anti Spy Detector & Camera Finder RF Signal Detector GPS Bug Detector Hidden Camera Detector for GSM Tracking Device GPS Radar Radio Frequency Detector https://www.amazon.com/dp/B07S2ZK2YF/ref=cm_sw_r_cp_apa_i_tuZNDbGPVW2NG


I've tried several different brands but this is one i have on hand.

Honestly I've never seen anything that even attempts to go over the sheer vastness of what goes on inside a cell. The best thing I can think of is to look over the movements and organization of phospholipids on the outer membrane, receptor tyrosine kinases, G-protein coupled receptors, and nuclear transcription factors. That just gives a very small sample of how many interactions the cell has with the outside environment. I know this is probably not what you're looking for, but this is currently the bible for cell/molecular biology:
http://www.amazon.com/Molecular-Biology-Cell-Bruce-Alberts/dp/0815341059

I would strongly recommend looking up the book Musicophilia: Tales of Music and the Brain by the late and inimitable Dr. Oliver Sacks. Also the book This Is Your Brain on Music: The Science of a Human Obsession by Prof. Daniel J. Levitin

Two things, (1) I'm going to recommend mostly books and not textbooks, since you're going to read plenty of those in the future. And (2) I'm going to only focus on the area of cognitive psychology & neuroscience. With that being said:

Beginner:

The Man Who Mistook His Wife for A Hat: And Other Clinical Tales By Oliver Sacks

Brain Bugs: How the Brain's Flaws Shape Our Lives By Dean Buonomano

Kludge: The Haphazard Evolution of the Mind By Gary Marcus

The Trouble with Testosterone: And Other Essays on the Biology of the Human Predicament By Robert M. Sapolsky

The Seven Sins of Memory: How the Mind Forgets and Remembers By Daniel L. Schacter

Intermediate: (I'm going to throw this in here, because reading the beginner texts will not allow you to really follow the advanced texts.)

Cognitive Neuroscience: The Biology of the Mind By Michael S. Gazzaniga, Richard B. Ivry & George R. Mangun

Advanced:

The Prefrontal Cortex By Joaquin Fuster

The Dream Drugstore: Chemically Altered States of Consciousness By J. Allan Hobson

The Oxford Handbook of Thinking and Reasoning By Keith J. Holyoak & Robert G. Morrison

I'd recommend Gullan and Cranston's The Insects: An Outline of Entomology.

A field guide is fairly regional, so you'll need to let us know where you're located!

I like this question.

Beginner:

• Neuroscience: Exploring the Brain (I don't like this text, but it's fairly accessible to beginners.)
  
  
• Auditory Neuroscience
  
  
• Musicophilia
  
  Student:
  
  
• Neuroscience
  
  
• MATLAB for Neuroscientists
  
  
• An Introduction to the Psychology/Physiology of Hearing (sorry, that was cheating)
  
  Expert:
  
  
• Principles of Neural Science
  
  
• Spikes
  
  
• Signal Detection Theory and Psychophysics
  

https://www.amazon.com/Quantum-Mechanics-Theoretical-Leonard-Susskind/dp/0465062903

There are a few decent books out there for beginners:

• Biology: A Self-Teaching Guide, 2nd edition
  
• Quantum Physics: A Beginner's Guide
  
• The Beak of the Finch: A Story of Evolution in Our Time
  
• Ecology: From Individuals to Ecosystems
  
• Cosmos
  
• The Selfish Gene

• The Emperor of All Maladies
  
  
• Sapiens: A Brief History of Humankind
  
  For a thriller treatment of infections diseases, the following are a nice read
  
  
• Microbe: Are We Ready For The Next Plague?
  
  
• The Hot Zone: The Terrifying True Story of the Origins of the Ebola Virus
  
  I'm inclined to also suggest the works of Simon Singh, to whom I was introduced by his book on math and cryptography - The Code Book. But he has also written about cosmology and "alternative" medicine. The later got him involved in a landmark libel lawsuit in the UK. For that reason, there is probably more than the usual bit of politics you'd expect in a popular science book. However, in the post-truth era of Donald Trump and company, that maybe fitting if bitter medicine.
  
  Edit: As someone who may not have the best scientific background, one might be prone to confuse science with pseudoscience. Even today, there is no shortage of low quality literature on UFOs and parapsychology. As such, Carl Sagan's The Demon Haunted World: Science as a Candle in the Dark is highly recommended.