r/bibliographies • u/[deleted] • Nov 27 '19

Mod Post How to learn our Math!

49 Upvotes

Hi,

So you want to learn math. Fantastic! Math is a wonderful but grueling subject, which is why here we make sure you can have all the resources at your disposal to make sure you either get that A in your class, make math really easy or make sure you really, really know your math to become a mathematician. But say you're our general audience, you're most likely an an Engineering student. Do you really need to learn about topology or abstract algebra? Nope. So this is how to use our math and our suggested guide. Enjoy!

 

Engineering

MechE/Aero/Astro/ChemE/Civil/CompE

Nuclear/Electrical/ECE

Sciences

Physics

Mathematics

Chemistry/Biology

Computer Science

3 comments

r/bibliographies • u/[deleted] • May 25 '20

Mod Post Quick Update

46 Upvotes

Hi all,

Not sure if people actually use this sub or if there are a few users that somewhat follow this sub lurking around

I know I have not been updating this sub with information as consistently possible. I do apologize but cannot in good conscience say that will change. I look at this as quality vs. quantity matter, and in my head it will always remain staunchly on the quality side.

I'm currently rewriting all the previous Bibs in LaTeX. This is taking time as I'm learning LaTeX for the first time. This is including verifying links again and as well as adding new links and resources. I'm also trying to find a good way to back up these Reddit Posts as well as making a collaborative medium in order to share these Bibliographies as a community/collaborative editing. This is based off of a comment by u/haelaeif found here. I am currently in the process of enacting some of their suggestions, and I do apologize to the user for never responding on their comment. Their first edit in their comment is partially solved by creating a subreddit discord, one of which I had previously and then deleted. Improvements in the discord will be stated in the official comment in the following days.

Any other issues can be raised within this post, I'll be responding to comments on this post.

If you want to join the discord early here it is if you've read this far words

I've updated a few links in the Physics Bibs.

Classical Mechanics is the current Work in Progress, as there aren't many Video Lectures or Notes for this field.

9 comments

r/bibliographies • u/[deleted] • Jun 18 '21

Mod Post There is a potential that this sub may be lost

34 Upvotes

As per this Reddit announcement they are removing subs in phase 2.

https://old.reddit.com/r/modnews/comments/o18ct9/creating_new_opportunities_for_future_community/

Phase 2:

Subreddits that meet all of the following will be removed [edited for clarity]:

  • Subreddits at least one year old as of 6/15/2021 AND

  • Subreddits with 0 posts in the last year (6/15/20 - 6/15/21) AND

  • Subreddits with 1-100 posts all time

We will not remove subreddits where the community creator has logged onto the site in the last 30 days (5/16/21 - 6/16/21) (I am not the community creator)

Admins will not clarify on their process, and as this subreddit meets the 1st and 3rd criteria I am planning on the worst as these are the Reddit Admins who don't ever do anything correctly.

I will post the link to the unfinished GitHub Repo and Bibliographies site here shortly once I get word back.

22 comments

r/bibliographies • u/[deleted] • Jan 27 '19

Mathematics Linear Algebra

34 Upvotes

"Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models. For nonlinear systems, which cannot be modeled with linear algebra, linear algebra is often used as a first-order approximation." -Wikipedia

Prerequisites:

Books:

Lectures:

Other Online Sources:

Problem Sets

Exams

Captain's Log

  • Added more online sources (11/28/19)

  • Added Exams, Problems and solutions (11/28/19)

9 comments

r/bibliographies • u/[deleted] • Mar 30 '23

Request Closing of the Project. Farewell.

33 Upvotes

Hello Everyone,

I'm sad to say that I'm making the hard decision to walk away from this project, and the greater reddit sphere.

I was diagnosed with a few mental and mood disorders and have had a rough 9 months. But I'm getting better and I'm improving, and I need to move on to better things and not feel attached to my old life and goals.

I thank everyone for their support, your grateful comments, and additions to the project.

I hope I've helped at least one person.

4 comments

r/bibliographies • u/[deleted] • Apr 12 '20

Physics Statistical Mechanics & Thermodynamics

29 Upvotes

Description:

"Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has many degrees of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. It can be used to explain the thermodynamic behavior of large systems." -Wikipedia

Preliminary:

I do want to say before a user starts this Bibliography, that this was one of the most difficult Bibs I've had to make in regards to the textbooks. For some reason, the textbooks pertaining to this field aren't highly regarded, nor are they usually well written. I have a hard time recommending any undergraduate textbook for Stat Mech or Thermodynamics:

  • Kittel & Kroemer hasn't been updated in over 40 years and the publishers are still asking nearly $150 for the book (at the time this bib was published). It is usually recommended in lieu of Schroeder.

  • Schroeder is typically used for intro Statistical Mechanics, and in most forums, is usually disliked, wherein most users refer to Kittel & Kroemer as their preferred textbook. This begins a cycle where one users hates Kittel & Kroemer and recommends Schroeder, another user comes in and recommends Kittel & Kroemer and thus continues the cycle.

  • Reif is known for it's usage for obscure notation, unnecessarily formality, and clarity issues. Some users state it is the best book, while others want to burn it in a fire.

  • Herbert B. Callen: Published and not revised since 1985. "In the preface to this second edition, Callen described his 25-year-old postulatory approach to thermodynamics and statistical mechanics as "now widely accepted". In fact, by the time of his second edition, his approach was completely outdated, because it springs from nineteenth-century ideas of thermodynamics in which concepts such as entropy were not understood. This means that Callen simply postulated the core quantities such as entropy and temperature with essentially no context, and without providing any physical insight or analysis. It might all look streamlined, but his approach will give you no insight into the difficult and interesting questions of the subject. Callen described his approach as rendering the subject transparent and simple; but his approach comes across as obscure. For example, in the early part of the book, he insists on repeatedly writing "1/T1 = 1/T2" for two temperatures that are ascertained to be equal, when anyone else would write "T1 = T2". And, for what he does write, the devil is often in the details that he tends to leave out. Even at the start, when Callen introduces the concept of work, he fails to say whether he is talking about the work done on the system, or by the system, leaving the reader to work that out for himself from some irrelevant comments about the mechanical work term −P dV. Callen's incorrect renditions of the Taylor expansion in an appendix seem to suggest, rather oddly, that he didn't understand the difference between "dx" and "Δx". His book includes a 20-page postscript in which he makes claims about the role of symmetry in thermodynamics; but, as far as I can tell, this section says nothing useful at all. I suspect that the reason this book is as frequently cited as it is said to be lies in its being used as the basis for a course by many lecturers who never learned the subject themselves, and hence don't reseal that the book's approach is outdated. If you really want to learn the subject, use the modern statistical approach, in which entropy is defined to relate to numbers of configurations. As far as readability goes, Callen's writing tends to omit commas; but this can make his sentences tedious to read, since the reader ends up having to make two or three passes to decode what some sentences are saying. (If you use few commas yourself, study a typical sentence in Callen's book: "the intermediate states of the gas are non equilibrium states for which the enthalpy is not defined". Callen is not singling out a special set of non-equilibrium states here; instead, enthalpy is not defined for any non-equilibrium state. He should have included a single comma, by writing "the intermediate states of the gas are non-equilibrium states, for which the enthalpy is not defined".) " -Vijay Fafat - UCR

Prerequisites:

Books:

Assignments

  • MIT OCW Undergraduate Statistical Physics I

  • MIT OCW Undergraduate Statistical Physics II

  • MIT OCW Graduate Statistical Mechanics I/Used in conjunction with Kardar Book I/Kardar Lecture I

  • MIT OCW Graduate Statistical Mechanics II/Used in conjunction with Kardar Book II/Kardar Lecture II

Lecture Notes:

  • MIT OCW Statistical Physics I

  • MIT OCW Statistical Physics II

  • MIT OCW Graduate Stat Mech I

  • MIT OCW Graduate Stat Mech II

  • Rochester Undergraduate Lecture Notes

  • Stanford Undergraduate Statistical Mechanics

  • Caltech Landing Page for all three terms

  • UCSC Landing Page for Undergraduate Stat Mech & Thermo

  • Rutgers Landing Page for Graduate Stat Mech for Rutgers

  • University of Cambridge - David Tong David Tongs' Lecture Notes are usually considered the best around

  • University of California, San Diego Currently a Work in Progress, though David Tongs landing page refers to them directly

  • MSU Graduate Statistical Mechanics/ Landing Page which has Lecture Notes, Problems and Solutions, and Midterms

  • MSU Graduate Statistical Physics, course from 2007-2016

Exams

  • MIT OCW Statistical Physics I

  • MIT OCW Grad Stat Mech I (Only Reviews, no actual tests)

  • MIT OCW Grad Stat Mech II (Only Reviews, no actual tests)

  • MSU Graduate Statistical Mechanics / Quizzes & Exams

  • Rochester Homework/Midterms/Final Exam

Lectures:

9 comments

r/bibliographies • u/[deleted] • Apr 02 '20

Physics Mathematical Methods in Physics

28 Upvotes

Preliminary:

Math methods is completely different than Mathematical Physics. Do not confuse either subject/field. Math Methods is not a field of physics, rather a field of internal instruction for physics majors.

Math Methods bridges the gap between Multivariable Calculus/Linear Algebra/Ordinary Differential Equations to complex mathematical areas which Physics Majors need to be fluent in, but not masters in. For example, most Physicists and/or majors do not need to be proficient in most areas of Real Analysis, Group Theory or Probability and Statistics. Some proficiency is required, but not to the level as Mathematicians and/or majors would need to be at. Math Methods essentially covers these areas to the degree of which you may require and not much afterwards.

In simple plain English, Math Methods takes out the bullshit and fluff that physicists don't require in their Mathematics.

Prerequisites:

Books:

Videos:

4 comments

r/bibliographies • u/[deleted] • Jun 21 '19

Mod Post I apologize for the Incursion

28 Upvotes

Hi,

You haven't heard from me or the mod team for a while. A few hours ago, we suspect a hacker to take over the account of u/MrsDonaldTrump and unsuccessfully tried to purge our subreddit. Due to certain parameters u/MrsDonaldTrump did no harm to the subreddit or its' content.

I foremostly apologize for this as I should have been checking in throughout the day on mobile or desktop but was out on personal business. I can't promise this can't happen again, but I've enacted even more security parameters before resuming development in this subreddit.

Thank you all for your support of this subreddit.

1 comment

r/bibliographies • u/[deleted] • Jan 25 '19

Physics Physics

28 Upvotes

Physics is the study of matter and energy, and seeks to understand how the universe works at its most fundamental level. The goal of physics is to come up with mathematical rules that can accurately predict and explain all of the various phenomena of our universe.

Prerequisites:

Studying physics at the high-school or conceptual level requires a good understanding of basic math and algebra. University-level physics requires calculus, since the mathematical laws of physics involve instantaneous rates of change. Readers who wish to learn physics at this level must understand limits, derivatives, and integrals, and should eventually study linear algebra, multivariable calculus, and differential equations after moving on to more advanced subtopics.

Where to Start:

Readers who wish to start learning physics should begin by obtaining an introductory textbook, which will typically cover basic mechanics, electricity and magnetism, and a few selected topics in modern physics. Introductory textbooks can be roughly divided by depth and difficulty into high-school, conceptual (algebra-based), and university (calculus-based) levels. Readers who are familiar with elementary calculus should start with a university-level text. Those wishing to make a serious study of physics should first learn calculus and then study a university-level text. It is very important to study the chosen textbook methodically, chapter-by-chapter, and it is especially important to solve the problems found at the end of each section. There is no substitute for solving many problems on your own when it comes to understanding physics.

You may wish to supplement your textbook reading with conceptual readings (like the Feynman lectures on Physics) and lectures appropriate to your level. These may help you think about your reading, but cannot replace studying a textbook deeply and solving physics problems. Once you finish the introductory text, you should be ready to move on to specialized subtopics - start with a more in-depth study of classical mechanics.

Books:

Articles:

Videos:

Other Online Sources:

Subtopics:

2 comments

r/bibliographies • u/[deleted] • Jan 31 '19

Mathematics Set Theory

26 Upvotes

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects.

Prerequisites:

Since set theory is a fundamental topic it doesn’t require any specific prerequisites. But, some mathematical maturity in the reader is needed to appreciate the relevance of some of the definitions and theorems. Depending on the set theory course, you may need first a course where you learn to write proofs. Or, that may be the emphasis of the set theory course itself.

Where to Start:

Readers who want to learn set theory should start with an introductory text book. A list of excellent choices is presented below. But, readers should be aware that there are a lot of books that teach set theory in “naive approach”. For a more complete understanding of the subject, an “axiomatic approach” must complement the naive approach. Since set theory is a first year undergraduate course, some readers might find set theory different to topics they have faced in high school. The sudden focus on proofs on seemingly “trivial” topics might be tedious for readers, but it is necessary to understand that rigorous proofs of fundamental results ensures integrity of mathematics as a whole. Readers might find taking written notes more helpful in understanding the subject.

Books:

Videos:

Other Online Sources:

This excellent paper by Kanamori talks about the historical development of set theory, what problems in mathematics gave rise to some of the ideas in set theory, and where the specific constructions came from. It's worth reading, or at least skimming

  • Frederique A short lecture notes on set theory by Frederique.

1 comment

r/bibliographies • u/[deleted] • Jan 25 '19

Mathematics Proof Techniques

23 Upvotes

Proof is essential to the structure of mathematics; it provides mathematical statements with a certainty that is impossible in virtually every other field of intellectual inquiry. A valid proof provides an absolute link between established axioms and truths of mathematics and a new piece of mathematical knowledge known as a theorem. Proficiency with these techniques is a prerequisite to the study of higher mathematics. This bibliography covers the basic methods that are used to contruct a proof of a theorem, while proof theory, computer-assisted proof, and other topics in mathematical logic are outside its scope.

Prerequisites:

Readers can study methods of proof without any prior knowledge. However, familiarity with basic propositional and first order logic may be helpful, since proofs are essentially informal arguments with an underlying formal logical structure. For example, one of the basic proof techniques is proving the contrapositive rather than the original statement of a theorem, and readers who have studied logic will immediately understand why the contrapositive is logically equivalent to the conditional statement itself. Many introductory proof textbooks will contain these aspects of formal logic, so a separate study is not strictly necessary.

It is difficult to demonstrate the methods of proof without having something to prove, and so different introductory texts will typically assume (or explain) some background mathematical knowledge. Readers should check that the sources they use do not assume too much knowledge beyond their current level; however this will not usually pose an insurmountable problem for those familiar with elementary mathematics and algebra.

Where to Start:

Readers wanting to learn how to construct proofs should obtain an introductory textbook. Proof techniques should be learned in two steps: first understand how the strategy works, then use that technique to prove simple mathematical statements until the proof strategy becomes second nature. For example, to understand proof by contradiction you must first understand the idea behind the technique - statements can only be true or false, so if you can demonstrate that it is impossible for a statement to be false by deriving a contradicton, then the statement must be true - then practice it by proving statements; the classic example of proof by contradiction is the proof that the square root of two is irrational: if you assume that the square root of two is a reduced fraction a/b, you can show that a,b must have the factor 2 in common, which contradicts the assumption that a/b is a reduced fraction, and therefore the square root of two must be irrational. Choose many simple mathematical statements and practice using each strategy several times.

Readers who complete a study of proof methods should understand the conditional structure of theorems, understand how to write concise proofs, and know the following proof methods: direct proof, proof by contradiction, proving the contrapositive, proof by exhaustion (cases), existence and uniqueness proofs, universal and existential quantifiers and counterexamples, proving biconditional statements, and mathematical induction. After completing this study, readers will be prepared to study formal mathematics, although it is advisible to study basic math through elementary calculus before beginning work on pure mathematics. Good places to start are real analysis, discrete mathematics, or number theory.

Books:

Articles:

Videos:

Other Online Sources:

Subtopics:

3 comments

r/bibliographies • u/[deleted] • Jan 25 '19

Programming LaTeX

22 Upvotes

aTeX is a typesetting language built on TeX that makes it very easy to produce high-quality documents, and is especially useful in the creation of mathematical and scientific works due to the ease with which mathematical formulae can be written. LaTeX is a simple markup language similar to HTML, although it can be extended with packages and with some effort the underlying TeX can be used like any programming language. This bibliography covers only the basics of using LaTeX; it does not cover the TeX typesetting language itself or the many packages that extend the functionality of LaTeX.

Prerequisites:

Getting started with LaTeX only requires a computer; all of the needed programs are free. It is a very simple language and requires no previous programming experience.

Where to Start:

Readers who wish to start creating documents with LaTeX should first install a LaTeX distribution and an IDE (Integrated Development Environment). The distribution contains the compilers that convert your LaTeX code into a well-formatted postscript or PDF file. The IDE is not strictly necessary but makes it much easier to create LaTeX documents. Follow these steps:

  1. Install a distribution of LaTeX. It is recommended that you install MiKTeX, a very popular distribution. The Windows installer can be found here. It is also possible to install this distribution on computers using Linux or Mac operating systems.

  2. Install an IDE. Readers who are familiar with Microsoft Word may wish to use TeXnicCenter, which has an interface that is very similar to a Windows word processor. Another choice that is good for beginners is Texmaker, which is also available for Linux and Mac.

While installing the IDE, you may be asked to provide the installer with the directory where your LaTeX compiler is located. If you've installed MiKTeX, the compiler location from the MiKTeX directory is \miktex\bin\latex.exe. You may also need to install a postscript viewer - a good open-source choice is GSview (install Ghostscript and then GSView). You may also want to install ImageMagick in order to convert picture files into the encapsulated postscript (eps) format required to include them in LaTeX documents.

Once you have your distribution and IDE installed, try creating a new document. A good first document can be found here. You'll see that the code is quite simple and similar to HTML, another markup language. The document consists of plaintext and simple commands of the basic form \command[optional_parameters]{argument}. Type in the code from the given link and compile it to a PDF file using the appropriate IDE command. A good rule of thumb is to compile documents two or three times; the compiler uses output from previous compilations to update links between different parts of the document, to insert appropriate numbers in enumerated lists, and for various other reasons. Try typing the following code into your editor and then compiling it to create your first LaTeX document:

\documentclass{article}

\begin{document}
Hello World!
\end{document}

To continue learning how to write LaTeX documents, readers may wish to go through "The Not So Short Introduction to LaTeX 2ε", an outstanding introduction to the language. As you gain experience, you will find additional packages to do more with LaTeX. These packages will significantly extend the functionality of LaTeX; it is even possible to create Powerpoint-like presentations using Beamer. Readers may eventually wish to learn how to modify LaTeX with new commands and environments, how to create their own packages, and how to modify LaTeX itself by learning more about TeX.

Books:

Articles:

Videos:

Other Online Sources:

Subtopics:

  • LaTeX: advanced formatting

  • LaTeX: BibTeX

  • LaTeX: Beamer presentations

  • LaTeX: creating new packages

  • LaTeX: TikZ

  • LaTeX: writing mathematics

2 comments

r/bibliographies • u/[deleted] • Mar 06 '19

Mathematics Real Analysis

21 Upvotes

"In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability." - Wikipedia.

Prerequisites:

Books:

How to Learn:

Lectures:

Subtopics:

This was posted by a user, whom I've banned due to being active participant in a quarantined community.

George Bergman's companion exercises to Rudin's textbook for Chapters 1-7.

Roger Cooke's solutions manual for Rudin's analysis

A subreddit devoted to Baby Rudin with further resources in the sidebar.

Tom Apostol's textbook

I find that Rudin is to Analysis textbooks what C++ is to programming languages. A little difficult at first, but with so many auxiliary sources that it becomes one of the best texts to learn from in spite of this.

2 comments

r/bibliographies • u/[deleted] • Jan 27 '19

Mathematics Multivariable Calculus

20 Upvotes

"Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one." -Wikipedia

Prerequisites:

Where to Start:

Readers who wish to study Multivariable calculus should pick a good introductory textbook and work through it chapter-by-chapter. These books tend to be very expensive, so readers may wish to choose a cheaper, older edition for self-study. It is very important to solve as many problems given in each section as possible - this is not just to test your reading; working (and sometimes struggling) with these problems is a necessary part of gaining proficiency in the techniques of calculus. Success will come with practice, and practice means solving problems.

At the end of a study of Multivariable calculus, readers should understand Limits and Continuity, Partial Differentiation, Multiple Integration, and the Fundamental Theorem of Calculus in Three Dimensions. This will prepare the reader to go on to study the mathematical laws of the physical sciences. Readers who wish to learn mathematics in more depth may wish to study analysis next, which covers the theorems and proofs behind calculus in far more depth. However, this will require an understanding of basic logic and the techniques needed to constructing proofs.

Books:

Videos:

Problems & Exams

Other Online Sources:

Subtopics:

  • Vector Calculus

1 comment

r/bibliographies • u/[deleted] • Jan 25 '19

Mathematics Precalculus

20 Upvotes

Precalculus encompasses mathematical knowledge useful to those who have taken high school algebra and are preparing to learn university-level calculus. Although readers who have taken algebra can move straight into calculus, it is recommended to learn the important background topics from precalculus ahead of time so that readers can focus exclusively on the concepts of calculus. The topics that should be studied in precalculus course can be grouped into three subjects: algebra, trigonometry, and analytic geometry (which should cover the definition of a function).

Prerequisites:

Readers should have a solid grasp of arithmetic before attempting to prepare for calculus. It is very important to have basic arithmetic facts memorized - if you struggle with arithmetic, you'll struggle with algebra. If you struggle with algebra, you'll struggle with calculus and so on until you decide that you are someone who is "not good at math". But there are no people who are inherently bad at math, only those who lack sufficient preparation. If you don't have the arithmetic tables memorized, it is very important to get a deck of flashcards and practice until they're automatic.

Readers should also have a basic familiarity with algebra. You should understand the basic rules of algebra and be able to manipulate equations, but may still need to write down every step in solving an equation. Algebra should be practiced diligently alongside the newer topics in trigonometry and analytic geometry. By the time you finish precalculus, you should be able to do algebra quickly and easily.

Where to Start:

Readers should obtain a precalculus textbook and work through each of the important topics chapter-by-chapter, solving as many problems as possible at the end of each section. As these books can be pricy, readers may want to purchase older editions, which will be far less expensive. A good preparation for calculus involves three topics - algebra, trigonometry, and analytic geometry. Standard precalculus texts do not focus on algebra, so if more practice with algebra is needed, it is recommended that you also pick up a supplementary text (see also the basic algebra bibliography). Readers who are new to mathematics may find some textbook explanations difficult - use supplemental videos and online materials to get additional information on topics you find difficult. But as with any mathematical technique, the only way to learn is by solving many problems - be sure to work as many problems as possible from your textbook.

More than anything else, the key to getting prepared for a college-level calculus is being able to manipulate algebraic expressions with fluency. Readers who struggle with symbols and equations, won't be focused on learning the underlying concepts in calculus. So it is very important to be comfortable with algebra before starting calculus. And the only way to do this is to practice algebra correctly - play with the algebra - until it feels natural. You should be able to look at equations like "2/3 x - 9 = 5" and see how these numbers move from one side to the other to end up with "x = 21". Practice your algebra diligently and you will set yourself up for success in calculus.

Trigonometry is encountered in calculus primarily because of its importance in physics and higher math - it is not essential to the concepts of elementary calculus, but will be encountered in problems and examples. Readers should understand what trigonometric ratios are and be able to explain what sine, cosine, and tangent mean using a right triangle inscribed within a unit circle. It will also be helpful to learn how to simplify trigonometric expressions using the most important identities.

In basic Algebraic Geometry, algebraic equations are studied by graphing them in the Cartesian coordinate system. Readers should at least learn the definition of a function, how to graph a function, how to interpret and work with graphs, and the functions associated with the conic sections (e.g. the parabola). There are a standard set of graphs and functions used in calculus as examples such as parabolas, hyperbolas, and the trigonometric functions, and readers should become familiar enough with these to be able to draw them on a graph from their algebraic form.

Books:

Articles:

Videos:

Other Online Sources:

Subtopics:

2 comments

r/bibliographies • u/[deleted] • Aug 30 '20

Mod Post I was not aware that the restricted setting disallows commenting

18 Upvotes

As Title, I set this sub to restricted months ago, not aware that it also disallows commenting. This was due to a number of spam posts that clogged up mod queue. Setting has been reverted.

Edit: I apologize for any inconvenience this may have caused.

4 comments

r/bibliographies • u/[deleted] • Mar 06 '19

Mathematics Discrete Mathematics

18 Upvotes

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic[1] – do not vary smoothly in this way, but have distinct, separated values.[2][3] Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets[4] (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics."[5] Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. - Wikipedia

Prerequisites:

Books:

Articles:

Videos:

Problems & Exam

Captains Log

  • Added in Problems (11/29/19)

0 comments

r/bibliographies • u/[deleted] • Jan 25 '19

Mod Post How to create new Bibliographies

18 Upvotes

Welcome to /r/bibliographies: a place to start learning any subject

The Purpose of this Subreddit

This subreddit is designed to help those who want to learn something new by providing lists of introductory sources on a wide variety of subjects. Our goal is to accumulate an archive of posts, which we call bibliographies, that collectively form an introduction to every single subject our readers might want to learn. And we want our bibliographies to cover every subject, not just academic topics; if there's something to know, we want to have a bibliography about it! Whatever your interests - science, art, entertainment, practical skills, crafts, culture, or hobbies - we want to help you start learning.

Using Our Bibliographies

Every post in this subreddit is a bibliography, each focusing on a certain area of knowledge, which we call the scope of the bibliography. Some bibliographies are very general in scope and are designed to give readers an overview of a subject as a whole - these are created for readers learning the subject from the beginning. Others are very specific, covering only a small portion of a subject in greater detail for readers who want to expand their expertise. But regardless of the scope, each bibliography contains advice and a list of resources (books, articles, webpages, and videos) for our readers to begin their exploration of the topic. Here is an example of a very general bibliography:

[Physics] Physics

As you can see, these bibliographies will tell you exactly what you need to know and what sources to use to begin learning. You will have the guidance you need to take the first few steps towards mastering a new subject. And if you have questions, you can always post them in the comments section of the bibliography, which is a great place for beginners to help each other and get advice from other redditors with more experience.

A Resource We Create Together

The bibliographies subreddit is a collaborative project. If you are using a bibliography and have suggestions or know of useful sources, please post a comment in that bibliography's subreddit. These comments are always helpful to us and help make the subreddit more useful to our readers. And anyone is welcome to start their own bibliography on any subject whether it is a favorite hobby, a profession, a research topic, or just to help readers learn something interesting. Just be sure to use the bibliography template and message the moderators if you need any help or guidance. All bibliographies are reviewed by moderators before being approved for the subreddit, so don't worry about making mistakes or being unsure of the format - we're all here to help each other create great bibliographies and help our readers learn!

Before getting started, please look over the wiki and read the FAQs. Thank you for visiting and have fun learning!

Frequently asked questions

Bibliography template

Directory of Bibliographies

If you have a bibliography request, questions, comments, or suggestions, please post them in the comments below!

1 comment

r/bibliographies • u/[deleted] • Dec 25 '20

Work in Progress Waves & Oscillations

17 Upvotes
Preliminary

This subsection will be quite small, due to two reasons; The course isn't taught at many schools, rather the course is wrapped up as a section in their Quantum Mechanics course, their Modern Physics course, Electrodynamics, or Classical Mechanics. Different Colleges and Universities teach their courses differently, so this subsection is to appease the general audience who have a separate course for Waves and Oscillations (or Vibrations). Users who do not, may continue onto the next physics Bibliography.

A vast majority of US universities (that I'm aware of) no longer have full courses on Waves and Oscillations, the one's I'm aware that have name power of are Cornell and MIT. Most other institutions wrap it up in either Modern Physics or Quantum Mechanics.

For the sake of my recommendations, I'll assume you're a U.S. undergraduate either in their 2nd or 3rd year taking a full Waves and Oscillations course.

Pre-Requisites
Books

  • R.A. Waldron - Waves and Oscillations - Archive link. As far as I'm aware it's a fairly conceptual book (only ~ 60 pages) but derives topics in W&O using PDE's and such. Seems like a decent book, and I've seen it recommend across a few forums and a quick scan seems like it does the job. Chapter 6 does seem outdated though (Network Theory) will need someone else to a-okay the outdateness as well.

  • David Morin - Waves and Oscillations Draft - Harvard Scholar link, from the same Morin that has a Classical Mechanics Book out with Thompson. It's in draft format from a new book that he's writing. I haven't seen many PDE's rather n-th order Linear ODE's

  • A.P French - Vibrations and Waves - MIT's book on said topic used in their version of the class at MIT, and possibly on OCW (will have to check on that). I'd imagine it's good enough, as it is used at MIT. Haven't done much checking on this book, but I recall his Introductory Physics book was pretty solid in any case.

  • Howard Geogri - The Physics of Waves - This is like a "textbook" textbook. Has a complete chapter on symmetries of physics.

  • M.I Rabinovich and D.I Trubetskov - Oscillations and Waves: in Linear and Nonlinear Systems - Russian/Soviet Era Textbook that will kick your ass. Has applications towards hydrodynamics and stochastic oscillations, in reference towards nonlinear oscillations and waves.

Lectures:
Lecture Notes:
2 comments

r/bibliographies • u/[deleted] • Dec 05 '19

Physics General Relativity

17 Upvotes

Prerequisites:

Books

Lecture Notes

Videos:

Problems and Exams

**Subtopics:**l

  • Subtopic - Bibliography does not exist

Captain's Log

  • 3/25/2020: Susskind Lecture link broke, re-added proper link

1 comment

r/bibliographies • u/[deleted] • Nov 26 '19

Mod Post Click this to see all our completed Bibs!

Thumbnail old.reddit.com
16 Upvotes
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r/bibliographies • u/[deleted] • Jan 25 '19

Mathematics Single-Variable Calculus

16 Upvotes

Calculus is a set of mathematical techniques based on applying the idea of limit to functions, which makes it possible to study the rate at which a function changes at one specific instant rather than just its average rate of change over a finite period of time. The techniques of calculus are the foundation of physical science, and so it is no coincidence that calculus and modern physics were born simultaneously through the work of Sir Isaac Newton and his contemporaries.

Prerequisites:

Readers who wish to learn elementary calculus must have an understanding of arithmetic and basic algebra (manipulating algebraic expressions and solving algebraic equations). It is helpful but not necessary to be familiar with trigonometry (sine, cosine, and tangent as ratios within the unit circle and their application to geometry) and analytic geometry (parabolas, hyperbolas, conic sections, and other related functions) - these can be learned while studying the calculus.

It is important to note that learning this topic is not nearly as difficult as its "scary" reputation might suggest. Do not be put off by the word "calculus" - all readers who have a good grasp of basic math and basic algebra will be able to learn its techniques. Understanding the ideas behind the techniques will require you to solve many problems, think about the concepts, and eventually study theorems, but anyone can learn calculus itself. Readers should think of elementary calculus as being merely the basic grammar of science.

Where to Start:

Readers who wish to study calculus should pick a good introductory textbook and work through it chapter-by-chapter. These books tend to be very expensive, so readers may wish to choose a cheaper, older edition for self-study. It is very important to solve as many problems given in each section as possible - this is not just to test your reading; working (and sometimes struggling) with these problems is a necessary part of gaining proficiency in the techniques of calculus. Success will come with practice, and practice means solving problems.

At the end of a study of elementary calculus, readers should understand functions, limits, continuity, derivatives, and integrals, and should also be familiar with trigonometric, exponential, and logarithmic functions as well as sequences and series. This will prepare the reader to go on to study the mathematical laws of the physical sciences. Readers who wish to learn mathematics in more depth may wish to study analysis next, which covers the theorems and proofs behind calculus in far more depth. However, this will require an understanding of basic logic and the techniques needed to constructing proofs.

Readers who wish to study the physical sciences or engineering will discover that elementary calculus is only the first set of techniques they must master - the next steps are to learn multivariable calculus and differential equations. Multivariable calculus extends the techniques of calculus to functions of many variables (for example, one can find the volume of a geometric shape by integrating over the interior of the three-dimensional figure). This should culminate in a study of calculus applied to vector spaces, also known as vector calculus. In the study of differential equations, readers will learn how to find functions that solve equations containing derivatives - and most of the universe's rules are written in the form of differential equations.

Books:

Articles:

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Other Online Sources:

Subtopics:

Calculus I (Differential Calculus) Standard Pathway Bibliography

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Intermediate:

Expert:

Lecture

Problems

Intermediate

Expert

1 comment

r/bibliographies • u/[deleted] • Apr 15 '21

Mod Post Bibliographies and Updates to be published by 8/15/2021

15 Upvotes

Bibliographies and Updates to be published by 8/15/2021

Mathematics:

  • Lie Algebra

  • Group Theory

Physics:

  • Nuclear Physics

  • Physics Bibliography to be split into Newtonian Mechanics, and Newtonian Electrostatics

  • Plasma Physics

  • Condensed matter physics

  • Optics

  • Modern Physics

  • General and Special Relativity to me moved out of WIP

Engineering:

  • Mechanical/Civil (Analysis): Engineering Statics/Mechanics of Materials/Dynamics

  • Structural Analysis is a maybe; dependent on completion of all "Mechanical" sets and then to be decided.

  • Mechanical (Thermal-Fluids): Engineering Thermodynamics/Fluid Dynamics/Heat and Mass Transfer

  • Mechanical/Materials: Engineering Materials

  • Electrical Engineering: Circuit Analysis

Things that are happening in the background:

  • LaTeX document is approaching nearly 60 pages

  • JabRef database is approaching 130 books

  • Citations are being re-run/links are being checked

  • Github Pages for the Bibliographies Project is off the ground

  • Github is now filled with Markdown documents of the project

  • Physics Bibliography is being re-written

  • Subreddit (/r/bibliographies) is being redone to streamline the end user experience.

  • Subreddit wiki has been updated to show a rough timeline

Please don't keep this as a binding document, I still have to complete this semester, 12 credits in the summer, and another 14 in the Fall. Updates will be slow but are coming.

0 comments

r/bibliographies • u/[deleted] • Nov 29 '19

Mathematics Tensor Calculus

15 Upvotes

“In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita it was used by Albert Einstein to develop his theory of general relativity. Contrasted with the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold. Tensor calculus has many real-life applications in physics and engineering, including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity) and quantum field theory.” -Wikipedia

Prerequisites:

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Articles:

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2 comments

r/bibliographies • u/[deleted] • Feb 19 '19

Languages Ossetian

15 Upvotes

Ossetian is an Iranian language spoken by roughly 500,000 people in Ossetia, a region that straddles the border or Russia and Georgia. It is distantly related to Farsi, Tajik, Dari, Kurdish and Pashto.

Prerequisites:

There are no prerequisites other than having an interest in Ossetian language and culture.

Where to Start:

A large bulk of Ossetian materials are found in Russian, but since it is rarely studied by English natives, resources for learning Ossetian are thus limited.

Don't worry though, there are still some very valuable resources available to learn the language, as shown below.

The first way to start learning Ossetian is to learn the alphabet. Ossetian is written in the Cyrillic Script, with a few additions of its own.

Ossetian is grammatically complex, especially when compared to other Iranian languages. The language has nine cases (nominative, genitive, dative, directive, ablative, inessive, adessive, equative, comitative), but lacks grammatical gender.

Videos:

Other Online Sources:

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