Embedded Files
Here is a collection of resources--textbooks, papers, lecture videos, talks, etc--that I have found uniquely helpful.
Meta: I think the most important resources I've clumsily gathered here can be found in "thinking and learning" and "writing". In particular, the lecture series by Richard Hamming and Judy Swan's work on scientific writing probably stands out the most, to me, in terms of their importance. Polya's lecture is an absolute gem too (provided above and also in "mathematics").
Gilbert Strang's lectures on linear algebra are also a much watch. Just really incredible stuff. And Frederic Schuller's lectures are also great.
research
research
On the process of becoming a great scientist.
Tinker early and often.
Get good feedback on your tinkering (e.g. ask others, visualize results, etc.).
Have more than one seed planted.
Ten simple rules for doing your best research, according to Hamming.
Public Communication for Researchers. YouTube channel with videos on writing, giving talks, etc.
Publish Your Research 101 (George Whitesides). Some great advice and insights regarding communicating your research.
Toward a science of simplicity. Ted talk by George Whitesides on simplicity.
The importance of stupidity in science. A short essay by MA Schwartz on the importance of humility and being comfortable feeling stupid while doing scientific research.
Clear Off the Table. Advice for making tables cleaner and more clear.
Surviving and Thriving in Higher Education. YouTube channel with a number of videos on topics such as choosing a research topic, writing a paper (quickly and effectively), preparing for job interviews, etc.
How to Read a Paper Efficiently.
1. Don't read article from beginning to end
2. Surveying the article
Read title and keywords
Read abstracts and conclusions
3. Phase II
Look at table and figures including captions
Read introduction
Read results and discussions
Read the experimental for more details
Write some notes to avoid rereading
Career Advice / Reading Research Papers. Lecture by Andrew Ng on some general career advice and advice for reading research papers.
I would extend all the great advice on reading papers to include one exercise that I also like to do. I like to sort of jokingly ask myself, "If I were forced to convincingly cite and/or use the results of this paper in my own research in some way, how would I do it?". Trying to impose or force the ideas of others into my own research--especially when they are seemingly very different research topics--often leads to ridiculous, silly, and stupid ideas. However, I've also found that trying to impose or force the ideas of others into my own research--especially when they are seemingly very different research topics--can sometimes lead to the most creative and interesting ideas. Thinking about it for a few minutes is a kind of low risk/high reward exercise. There is plenty of high-impact research out there that is mostly a result of (effectively) making connections between seemingly different fields. It also helps you check your understanding of the paper you've read and how it fits into the broader context of scientific research.
To be clear: I am not advocating Frankensteining together concepts from different fields for the sake of doing something different. But if this generates a promising research idea that, as an added benefit, also brings together concepts from different fields, then in some ways the research will likely be all the more impactful.
Both google scholar and research gate allow you to follow people and set up notifications for when they've published new papers. Not only is it good for you to make account(s) and follow those in your field who are doing exciting, important, and inspiring research, but making these accounts (and adding your papers) will also allow you to share your research more broadly and efficiently.
Thomas Kuhn. The Structure of Scientific Revolutions.
I have some mixed feelings about this work, but it is highly influential and provides an important perspective.
Funding, fellowship, and research opportunities for graduate students:
Graduate Student Funding Opportunities (JHU repository). "...continuously updated repository of federal and private funding opportunities that are intended for graduate students..."
Grants in Aid of Research Program. Grants up to $1,000 for travel expenses or non-standard lab equipment.
CCDC Army Research Laboratory Research Associateship Program.
Institute for Mathematical and Statistical Innovation Summer Internship Program. If this link is dead, then check their home page (https://www.imsi.institute/). There are generally summer internships available. The topics are often in computational mathematics, data science, machine learning, etc.
Small Business Innovation Research (SBIR) and Small Business Technology Transfer (STTR) programs. Grants for seed money toward starting a company or transitioning your research to commercial applications.
RECS. Research experience in carbon sequestration. "RECS is the premier carbon capture, utilization and storage (CCUS) education and training experience and career network for graduate students and early career professionals in the U.S. Sponsored by the U.S. Department of Energy, RECS is an annual intensive program that combines classroom instruction with group exercises, site visits, communications training, and hands-on field activities covering science, technology, policy, and business topics associated with CCUS deployment."
Research opportunities for undergraduates:
I like to keep my summaries to 2-5 sentences. Maybe: what they did, how they did it, important results. And I tend to store summaries about a topic together in a single google document. This makes writing introductions much easier and more natural.
Getting funding and writing proposals
Some folks from NSF have noted (I'm paraphrasing):
Although it may take some time to receive a response, it is generally a good idea to send a 1-page white paper / research proposal summary to program managers (their email addresses can generally be found on the program home page), to get some initial feedback, before sending a finished and polished proposal.
They can let you know if the proposal is likely to be funded and what they see as strengths or weaknesses in the proposal.
NSF CAREER resources (but this advice is more broadly applicable for proposal writing and career advice, in general)
2021 NSF CAREER: Past CAREER Awardees Discussion.
Communicate with program managers early and often
Go into NSF's award search; see what has been funded; can search by directorate and year
Get outside help; ask senior people in your field for advice
Education portion: identify a need, motivate why addressing this need is important, explain why you are uniquely suited for addressing this need, have a plan
Do you have buy-in from potential partners? (Use partnerships). How are you going to get people to show up?
Need to be outside of regular faculty activity, but not extreme
Approach education plan with same rigor that you approach research plan; does not necessarily need to be as "novel"
Show you are a unique person that will have a lasting impact
Be fold in your ideas and be rigorous
Grab attention upfront; make a strong case in the first 2-3 pages
Make assessment and measures of success explicit
Why You Should Volunteer to Serve as an NSF Reviewer.
Game Changer Academies. Partnered with the CMMI division of NSF. Panel fellows gain expertise on cognitive bias, group dynamics, cultural norms, discussion facilitation, conflict, and how peer evaluation pressures impact merit-review processes. Panel Fellows contribute as regular panelists in future CMMI review panels.
Merit Review Process. An overview of the review process at NSF.
NSF Rotator Programs. NSF offers a chance for scientists, engineers, and educators to join them as temporary program directors--called rotators.
Postdoc funding opportunities and training grants
Congressional Science Fellowships. Interesting opportunity for postdocs looking to help inform public policy. APS.
In general, getting jobs and funding requires story telling and self-promotion.
People don't just hire qualifications, they hire a colleague. Answer: who are you as a person?
People don't just fund a specific project, a list of tasks, or impacts. They also fund people. Answer: who are you? why are you well-suited for this work? how did you get here? where are you going? how does this project fit into your career trajectory and how will your career help the community as a whole?
Tuomas Sahlsten. Some research tips.
Zotero. An open source software tool for organizing and sharing references.
thinking and learning
thinking and learning
Take the world from another point of view (Feynman) "What witches do we believe in now?".
While we're on the subject of Feynman: The Meaning of It All: Thoughts of a Citizen-Scientist and Surely You're Joking Mr. Feynman both contain deep and practical advice for careful, critical thinking and truth finding.
The Architecture of Complexity. Paper by Herbert Simon on how systems are generally conceived by building up hierarchies of stable, modular, and (in some sense) self-contained components.
Charles Pierce. Philosophical Writings of Pierce.
Learning to Learn, Richard Hamming (lecture series)
"When I get stuck on something, I ask myself: 'what would an answer look like if I had it?... What does it really depend on?'"
I enjoy all of this lecture series, but Hamming's take on AI is particularly interesting. It feels like a fresh perspective despite being decades old.
There is also a book to accompany this excellent lecture series: The Art of Doing Science and Engineering.
Thinking, Fast and Slow
Think Twice: Harnessing the Power of Counterintuition
The Signal and the Noise
Outliers. A talk by Malcolm Gladwell about why some people succeed and others don't.
David Epstein in Conversation with Malcolm Gladwell. Malcolm Gladwell interviews David Epstein on his book "Range" where he investigates the tradeoff between early specialization and trying a broader range of things.
Where Good Ideas Come From. Very nice google talk by Steven Johnson. There is an associated book. It exposes and corrects some misconceptions about how ground breaking ideas are born and cultivated.
Antifragile. Talk by Nassim Nicholas Taleb.
Skin in the Game. Talk by Nassim Nicholas Taleb.
An Enquiry Regarding Human Understanding, David Hume (audiobook)
Some Daniel Dennett talks about evolution, thinking, free will, and consciousness (there is a book associated with a few of them as well)
Grit: The Power of Passion and Perseverance
Focus on continual improvement; the little things build up over time
Show up
Deliberate practice:
Be intentional: have a specific goal
100% focus; practice with great effort
Seek quality feedback
Reflection/refinement
How to use the Feynman technique
Pick a well defined topic
Write an explanation of the concept in a very simple language
Find trouble spots: where is it difficult to explain the concept simply
Review trouble spots
Simplify again; try to teach to a novice
P.S. In my opinion, explaining your research to a "novice" (in the sense that they are outside your field) is one of the most powerful ways to spark creativity. If the person is near to your field, chances are they will have ideas that you find both fresh and reasonably practical. These ideas are good for getting unstuck. If the person is far from your field, there may be a greater chance that they have or inspire a radical idea. While most radical ideas are impractical and a waste of time, there are a rare few that can lead to breakthroughs and truly great work.
One really interesting insight from this talk: it is sometimes good to visualize yourself failing--not as a source of discouragement, but so that you can anticipate and remove obstacles ahead of time. Kelly McGonigal suggests the following exercise (I'm paraphrasing a bit):
Ask: what is my goal?
What would be the most positive outcome?
What action will I take to reach this goal?
What is the biggest obstacle?
When and where is this obstacle most likely to occur?
What can I do to prevent this obstacle?
What specific thing will I do to get back to my goal when this obstacle happens?
Adam Grant and Malcolm Gladwell: Originals—How Nonconformists Move the World
It is really interesting to hear Adam Grant talk about considering college admissions as an ensemble rather than the prospective students as individuals; in other words, he seems to suggest it is more important to have a mix of students with different backgrounds, character, etc., than it is to simply have the top individuals.
This insight is likely broadly applicable. For instance, companies aspire to hire the best people, but they should also take care to hire different types of people as well (obviously in a way in which their differences are complimentary).
"Argue as if you're right. Listen as if you're wrong."
The Ghost Map. Google Talk by Steven Johnson (there is an associated book).
Some key takeaways (for me, anyway):
Communication of your idea is at least as important as the idea itself. If you can't properly convey and convince then you can't make a difference. Further, visual communication is very important.
Collaboration is almost necessary.
Branching out into different hobbies/interests is important.
What Technology Wants. Google Talk by Kevin Kelly. He develops a very nice analogy between technology and evolution.
The Finite and Infinite Games of Leadership. Talk by Simon Sinek.
Most Leaders Don't Even Know the Game They're In. Talk by Simon Sinek.
Freeman Dyson on meeting Fermi.
"Give me four free parameters and I can fit an elephant. If you give me five I can wiggle its trunk."
Daniel Dennett's Thinking Tools
“Absorb what is useful, discard what is useless and add what is specifically your own.”
- Bruce Lee
writing
writing
Whitesides' Group: Writing a Paper. Concise. A must-read.
Style. Toward Clarity and Grace. I am a huge fan of this work. It has a lot of concrete techniques and examples for writing clearly.
G. Gopen and J. Swan. The Science of Scientific Writing.
You'll notice more Judy Swan resources below. In my opinion, she has, by far, the absolute best advice on scientific writing (and her ideas generalize to other forms of communication, i.e. giving talks, as well).
Scientific Writing: Beyond Tips and Tricks. Really excellent talk by Judy Swan.
"Scientists are professional writers."
Words are arbitrary; text/words don't have fixed meanings. They have interpretations. Interpretations come from readers. There are an infinite number of interpretations. Have empathy for your reader. Put yourself in your reader's shoes. It takes energy to read and reader energy is finite.
Bad scientific writing: writing which takes a disproportionate amount of energy to figure out what it's all about.
Use emphasis to (skillfully) direct the reader's energy toward the most important points and contributions. This comes from, in large part, structure.
Main clause <=> most important point.
Placing something at the end of the sentence emphasizes it.
Increasing the length of a sentence can emphasize it as a whole (relative to other sentences in the same paragraph/section).
Use repetition.
In Praise of Technique. (short) Ted Talk by Judy Swan. Focuses on active/passive voice, "whose story?", and agency.
How to Write a Great Research Paper.
Have an Idea => Write a Paper => Do the Research.
Four sentence abstract: state the problem; say why it's an interesting problem; say what your solution achieves; say what follows from your solution.
"Intuition is primary."
Johusa Schimel. Writing Science: How to Write Papers that Get Cited and Proposals that Get Funded.
"As a scientist, you are a professional writer." I could not agree more.
How to Write Research Articles that Readers Understand and Cite.
writing clarity calculator. An associated text analysis tool which scores how concrete the writing is (# of examples), amount of active voice, percentage of jargon, etc.
Articles with short titles describing the results are cited more often.
How to get a paper published in a high impact journal. Some good advice for grabbing an editor's attention and getting your article out to review (at a good/high-impact journal).
Title and abstract are important. This may be all the editor reads.
"Should work like a marketing tool." Summarize key points/findings. State why they're important.
"Introduce topic; state problem; summarize findings; demonstrate broader impact."
Have a sharp focus to your story: "No more than 3 key messages."
"Pick your journal ahead of time." I don't think it is nearly this simple in practice, but I do agree with the spirit of this statement. You should have a balance between writing the paper you would like to write (because (a), in some sense, your audience isn't even 100% sure what it is that they want and (b) they will probably enjoy reading it more if you've enjoyed writing it) and writing a paper for a specific audience / specific journal.
Cover letter is important.
Address editor-in-chief by name
1 page only
Say why they should review it: why it fits into the journal (reference journal scope, use keywords); why the journal readership would find it important; how is it novel. Can support these things by using previous work published by the journal.
I was also given some related advice by someone who is quite successful at publishing in high impact journals. Their suggestion: add a flashy, cool, and informative figure. The figure does not need to be technical (in fact, it probably shouldn't be. The idea is to grab attention and give a high-level idea of what your research is. It is hard to do both that and be super technical). Then hire a professional artist (preferably one who specializes in producing scientific figures) to create it. This is enticing to the editors of the journal in a number of ways. For one, it shows that you are a professional and know how to present your research in a compelling way. It also shows that you have confidence and believe strongly in the quality of the work. Otherwise, you probably wouldn't have invested in a professional artist. These things of course don't guarantee that they'll publish your work, but it will make it far more likely that you will make it out to review, which, even if their decision is to not publish your work, will still be beneficial in a number of ways. Good journals tend to have good reviewers. And good reviewers can really help the quality of your paper when it is eventually published.
Strunk, White, and Kalman. The Elements of Style.
Essays and books on writing well. The mechanics community weighs in on good resources for writing.
Weitzlab Guide to Good Paper Writing. A nice, concrete, modern guide to scientific writing.
Advice on Writing Papers. Terence Tao.
R. Murray. Skillful Writing of an Awful Research Paper.
Successful Letters in Physical Review Letters. Talk by Serena Dalena, Associate Editor.
Cover letter...
Two paragraphs
Quickly, why you've done this work and why it's important.
Like abstract but shorter. Focus on why instead of how.
"Why results are new and important"
If there is work that is similar, mention what about yours is different and why the differences are important
visualization
visualization
Fundamentals of Data Visualization. Ebook by Claus O. Wilke.
Dataviz Books Everyone Should Read.
E. Tufte. The Visual Display of Quantitative Information.
D. McCandless. Information is Beautiful.
gnuplot. Beautiful graphics. Interfaces well with LaTeX.
matplotlib. Python library for data visualization.
PyPlot.jl. Julia version of matplotlib.
Scientific Visualization: Python + Matplotlib. Free book on scientific visualization with many beautiful examples.
Plots.jl. Julia package for data visualization.
Inkscape. Tools for annotating, drawing, and editing figures using vector graphics.
Mathematica.
geogebra. Excellent for visualizing and analyzing geometric constructions: points, graphs, parametric curves, surfaces, parametric surfaces, etc.
D3. JavaScript library for data visualization. Powerful, but has a learning curve. Well-suited for data-driven animations and interactive visuals.
Observable. Apsires to be the github of visualization.
presentations and "talks"
presentations and "talks"
How to Speak. Talk by Patrick Winston.
How to give a great talk. Simon Peyton Jones. Practical advice for delivering engaging talks.
posters
posters
How to create a better research poster in less time (including templates)
Designing Effective Research Posters. A talk by the Global Communication Center at CMU.
collaboration
collaboration
Meeting with and keeping groups organized
mathematics
mathematics
In general, Rudin and Kreyszig are two of my favorite writers when it comes to mathematics texts. Kreyszig tends to be more accessible to the novice while Rudin approaches topics with more depth; both write with excellent clarity.
Linear algebra (MIT) (lecture videos). (legendary) Lecture series by Gilbert Strang. Probably the best lectures on linear algebra that I've ever seen. Others seem to agree.
Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Another excellent lecture series by Gilbert Strang.
J. Michael Steele. The Cauchy-Schwarz Master Class.
An excellent introduction to an important (!) inequality. It has a great deal of exercises (with solutions) that help the reader get comfortable with applying CS to derive other inequalities. It develops proofs gradually and gives the reader some intuition as to how both the theorem and proof could have been discovered. In this way, this book could also serve as an introduction to mathematical thinking and proving results. In addition to its practicality, it is an enjoyable read.
G. Polya. How to Solve It.
Polya on teaching and problem solving techniques. (Lecture video). I highly recommend this. Polya really hits on the artistic energy, imagination, and creativity that goes into problem solving.
Euclid's Elements is still an excellent read.
R. Trudeau. Introduction to Graph Theory.
In addition to being a gentle introduction to graph theory for those with no prior knowledge of it, this book is also meant to be accessible to novices in mathematics. It could also serve as an introduction to mathematical thinking, basic logic, proofs, etc.
M. Hamermesh. Group Theory and Its Application to Physical Problems.
This introduction to group theory is ideal for graduate level engineering and physics students.
M. Tinkham. Group Theory and Quantum Mechanics.
I particularly enjoyed the way representation theory was presented.
J. Alperin and R. Bell. Groups and Representations.
M. Golubitsky and D. Schaeffer. Singularities and Groups in Bifurcation Theory.
This compliments S. Strogatz's text/course quite well I think. This book introduces bifurcation theory in a way that is a bit less example driven (though still has great examples) and goes deeper into bifurcation theory. Having some knowledge of differential geometry (at least some comfort level with smooth manifolds) or advanced calculus, and group theory helps.
S. Abbott. Understanding Analysis.
Excellent introduction to real analysis and proof-based mathematics in general.
A. Rozanov. Probability Theory: a Concise Course.
An accessible and concise introduction to probability theory. Good for independent-study.
The probability channel. Excellent YouTube channel by Nicolas Lanchier with courses on undergraduate probability, graduate probability, and stochastic modeling.
Associated book: N. Lanchier. Stochastic Modeling.
M. do Carmo. Differential Geometry of Curves and Surfaces.
One of the best texts I've found on the topic. Requires some mathematical sophistication.
Discrete Differential Geometry. A set of course notes by Keenan Crane. One of my favoriate lecture series.
Lectures on Geometrical Anatomy of Theoretical Physics. An excellent introduction by Frederic Schuller to the fundamentals of modern mathematics most relevant to physics.
J. Milnor. Morse Theory.
I have yet to find a version where the typesetting is great, but if you can get past that, this is one of the best texts I've encountered on Morse theory.
Y. Matsumoto. An Introduction to Morse Theory.
A clear and accessible introduction to Morse theory. This text does not require an of mathematical sophistication and there are many good examples (!).
Flatland and Surreal Numbers are novellas that remind us math can be fun and whimsical.
J. Conway. Sphere Packings, Lattices and Groups.
M. Lighthill. An Introduction to Fourier Analysis and Generalized Functions.
M. Greenberg. Applications of Green's Functions in Science and Engineering.
One of the better introductions to Green's functions that I've come across.
T. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
A clear introduction by one of the masters of FEM.
L. Grady and J Polimeni. Discrete calculus: Applied analysis on graphs for computational science
This book fills an interesting niche and has a nice perspective in that it makes concrete connections to other mathematical branches, concepts, tools, etc. Should be reasonably accessible to graduate-level scientists and engineers.
Three part lecture series by Mark Newman on graphs and networks...
Adaptive MCMC for everyone. Talk by Jeffrey Rosenthal.
Real analysis (Harvey Mudd) (lecture videos). Very nice lectures by Francis Su.
Nonlinear dynamics and chaos (Cornell) (lecture videos). Lecture series by Steven Strogatz. These lectures and his book are an excellent introduction to nonlinear dynamics and chaos from one of the masters of the field.
His book on nonlinear dynamics is excellent.
Complexity Explorer. (Santa Fe Institute). Free online courses on nonlinear dynamics, chaos, fractals, renormalization, game theory, diff. eq., and more.
Chaos (Jos Leys). A visual (and gentle) introduction to chaos.
Dimensions (Jos Leys). A visual exploration of geometry and dimensions.
Information theory, pattern recognition, and neural networks (Cambridge).
Visual Group Theory (Clemson). A visual introduction to group theory and lecture series by Professor Macauley. Cayley graphs are a much nicer way to understand a group's structure than pushing symbols around.
This lecture series is based on the book: Visual group theory by Nathan Carter. I haven't read it cover-to-cover, but what I have read has been excellent for getting a visual intuition for group theory. In particular, I found the way that concepts such as products, quotients, homomorphisms, etc, are communicated using Cayley diagrams to be very helpful.
Advanced Linear Algebra (Clemson). Another lecture series by Professor Macauley.
S. Axler. Linear Algebra Done Right.
Judson, T., Beezer, R. Abstract Algebra: Theory and Applications. Free Ebook on abstract algebra.
(Elementary) Representation Theory. A set of gentle and concise lectures, by MathDoctorBob, on representation theory to get your feet wet.
Representation theory and geometry. Very nice talk by Geordie Williamson, "a recurring theme is the appearance of geometric techniques in seemingly algebraic problems".
A gentle introduction to group representation theory. A good primer for representation theory by Peter Buergisser.
Differential Geometry (ICTP). Claudio Arezzo. There are many lecture series available online on differential geometry, but so far, this is probably my favorite.
Differential Geometry (UNSW). A unique perspective on geometry and mathematics. These lectures also touch on a topic which is not often discussed: projective geometry.
Geogebra. An excellent calculator / programming language for geometric constructions.
Differential Geometry (The WE-Heraeus International Winter School on Gravity and Light). A nice set of lectures by Frederic Schuller on differential geometry with an emphasis on its application to general relativity.
Topology and Geometry. Excellent lecture series by Tadashi Tokieda.
Unexpected Shapes. Super condensed version of the first lecture.
Project Euler. Series of challenging mathematical/computer science problems.
ICTP Mathematics. YouTube channel that clearly presents a wide array of somewhat advanced topics.
PDES and functional analysis. It can be difficult to find a good PDEs course on YouTube. This is one of the good ones.
Graduate Mathematics. YouTube channel.
3blue1brown. (excellent) YouTube channel.
What makes people engage with math. Ted talk by Grant Sanderson. Great resource for anyone that is interested in teaching.
Mathologer. YouTube channel.
Why don't they teach this simple visual solution? (Lill's method). Makes a connections between the roots of polynomials, geometry, and origami.
blackpenredpen. YouTube channel.
Michael Penn. YouTube channel.
Numberphile. YouTube channel.
Tadashi Tokieda on Numberphile. A playlist of one of my favorite contributors, Tadashi Tokieda.
Necklace splitting. Noga Alon.
Miracles of Algebraic Graph Theory. Really nice talk by Daniel Spielman.
The solution of the Kadison-Singer problem. Daniel Spielman.
Understanding Networks through Physical Metaphors. Daniel Spielman.
Sparsification of Graphs and Matrices. Daniel Spielman.
The Laplacian Matrices of Graphs. Daniel Spielman.
Sarada Herke. YouTube channel on Combinatorics and Graph Theory.
You Could Have Invented Homology. A YouTube series that gently and visually introduces homology and algebraic topology.
D3 Graph Theory. Learn graph theory interactively.
Calculus (Coursera course). UPenn has a really nice Calculus series on Coursera. It is accessible, but also touches on some deep topics. There is even a course on discrete calculus.
Prof. Robert Ghrist is an excellent educator, in general: website, YouTube Channel.
The Essence of Linear Algebra. A 3Blue1Brown series. Gentle and visual introduction to the foundations of linear glebra.
W. Thurston. On Proof and Progress in Mathematics.
W. Thurston and J. Weeks. The Mathematics of Three-Dimensional Manifolds.
A Mathematical Journey through Scales. Martin Hairer.
Category Theory for Programmers. Bartosz Milewski.
Differential Topology. Lectures by John Wilnor.
princetonmathematics. YouTube channel.
Liquid Argon at 100 K; simulated using this code.
Hard disk packing simulation
Hard disk packing simulation
statistical mechanics and thermodynamics
statistical mechanics and thermodynamics
T. Hill. An introduction to statistical thermodynamics. Courier Corporation, 1986.
The foundations of statistical mechanics and the construction of ensemble theory are very clearly laid out. The mathematical techniques used are relatively simple--which keeps the physics front and center. It also clearly establishes the power and simplicity of the mean-field approach.
The author has also written other books on statistical mechanics and thermodynamics that are good.
R. Swendsen. An introduction to statistical mechanics and thermodynamics. Oxford University Press, USA, 2020.
This introduction makes a lot of nice connections to computer methods and computational statistical mechanics--in both the main text and the exercises.
J. Sethna. Statistical mechanics: entropy, order parameters, and complexity. Vol. 14. Oxford University Press, 2006.
This book is really unique in that it is accessible, touches on a lot of topics that most statistical mechanics introductions do not get to, and is also deep.
J. L. Ericksen. Introduction to the Thermodynamics of Solids.
Deep, yet requires only the knowledge of simple mathematical tools. Also one of the few thermodynamics texts that focuses on solids.
H. B. Callen. Thermodynamics and an Introduction to Thermostatistics.
R. Shankar. Quantum Field Theory and Condensed Matter: An Introduction
Also a nice introduction to path integrals.
R. K. Pathria, and Paul D. Beale. Statistical Mechanics. Elsevier, 2011.
This text provides a nice overview of some important and powerful mathematical tools that can be used in statistical mechanics. Because of this, it helps coming in with some amount mathematical sophistication.
M. Deserno. Legendre Transforms.
Deserno is an excellent writer in general and this is a nice reference for a topic that can be very confusing to novices studying thermodynamics.
Microcanonical and canonical two-dimensional Ising model: An example. Speaking of Deserno, in this preprint he points out an often underappreciated and subtle detail in statistical mechanics: different ensembles often give different results. While we usually wave our hands at this and say "thermodynamic limit", the differences can sometimes be important--especially when we are dealing with critical points, phase transitions, etc.
MIT. Statistical Mechanics I: Statistical Mechanics of Particles (lecture videos)
MIT. Statistical Mechanics II: Statistical Mechanics of Fields (lecture videos)
Stanford. Statistical Mechanics (lecture videos). Lecture series by Leonard Susskind. They are a nice combination of accessible and deep--although obviously not comprehensive.
Statistical Mechanics (lecture videos). John Preskill.
Statistical Mechanics: Algorithms and Computations (Coursera course)
There is also a book by the same title which compliments the course.
I recommend the book, especially to beginners in computational statistical mechanics. The book (and course) serve as a lucid and focused introduction to a topic that is often thrown in to statistical mechanics texts as an afterthought. While it is true that many modern texts on statistical mechanics get the computational part right, since it isn't the main focus, none of them present computational statistical mechanics in such a focused way.
Nonequilibrium statistical mechanics (Chris Jarzynski)
Nonequilibrium statistical mechanics. Lecture series by V. Balakrishnan (IIT Madras). It is rare to find such a nice introduction to nonequilibrium statistical mechanics (that is also free to watch).
Thermodynamics as Control Theory. Talk by David Wallace.
Foundations of Statistical Mechanics (summer school lecture series)
The Scientific Papers of Gibbs. Dense but undoubtedly worth the effort.
Carnot. Reflections on the Motive Power of Heat.
Still illuminating. The kind of work that will help you to appreciate the subject of thermodynamics in an entirely new way.
Ludwig Boltzmann. Lectures on gas theory.
Boltzmann is sometimes a difficult read and it isn't always easy to find English versions of his work. However, he was a very original thinker and his work is well worth the read.
Theory-based Discovery of Highly Reversible Phase-transforming Materials. Talk by Richard James.
The Physics of Complex Systems. Lecture by Mark Newman.
ParaMonte. Parallel Monte Carlo library.
The Beginning of the Monte Carlo Method. Metropolis.
Michael Betancourt: Scalable Bayesian Inference with Hamiltonian Monte Carlo. Talk by Michael Betancourt on Hamiltonian Monte Carlo.
Metropolis Algorithm javascript program, by Jeffrey Rosenthal. A nice interactive introduction to MCMC.
lattice Boltzmann method
lattice Boltzmann method
S. Succi. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond.
It is difficult to find a good text on the lattice Boltzmann equation and the lattice Boltzmann method. This is one of the good ones. It is sometimes a little difficult for the beginner and it touches on many different topics, but it is clearly written and well worth the read.
DA Wolf-Gladrow. Lattice-Gas Cellular Automata and Lattice Boltzmann Models.
This is probably my favorite text on LBM. It is a gentle introduction. It constructs LBM in a way that is more chronological than it is purely logical, but I don't think it ends up hurting the book too much. In fact, it is interesting to learn about LGCA (if you choose to read those chapters). This book is also the best (IMO) in terms of developing a clear understanding of LBM as a finite difference approximation of the lattice Boltzmann equation--which is a very important concept, I think.
The Lattice Boltzmann Method: Principles and Practice.
I mentioned this lecture series before. Not all of it is relevant to LBM, but in lectures 23-27 he derives the Boltzmann-Maxwell distribution, derives the Boltzmann equation, and also works through some examples where it can be approximately solved by linearizing the collision term. It can be very helpful in terms of understanding the theory and foundations of LBM.
A. Vikhansky. Lattice-Boltzmann method for yield-stress liquids.
origami
origami
Anything by Robert Lang, but in particular:
Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami
Origami Design Secrets: Mathematical Methods for an Ancient Art
E. Demaine and J. O'Rourke. Geometric folding algorithms: linkages, origami, polyhedra.
P. Engel. Folding the Universe.
More narrative and artistic, and less mathematical. However, this is a very important perspective in origami, even if one is primarily focused on mechanics.
T. Hull. Project Origami.
Folding a New Tomorrow (talk). Thomas Hull.
Atomistically Inspired Origami. talk by Richard James.
Science from a Sheet of Paper. talk by Tadashi Tokieda.
The Geometry of Origami. talk by Erik Demaine.
Note: this is part 1, but parts 2-4 are also on youtube.
Paper and Stick Film. This presents a very interesting (and realistic) approach to problem solving. Ron Resch describes how he develops various origami constructions through a sort of intelligent and deliberate tinkering.
Engineering with Origami. Veritasium (w/ Lang and Howell). Covers a lot of very interesting and important applications for origami.
Huffman. Curvature and Creases--A Primer.
This list is by no means comprehensive, but there are many good papers by (in no particular order): Larry Howell, Robert Lang, Thomas Hull, Christian Santangelo, Itai Cohen, Jesse Silverberg, Erik Demaine, Tomohiro Tachi, Martin van Heck, Scott Waitukaitis, Evgueni Filipov, Mark Schenk, Simon Guest, Glaucio H. Paulino, Suyi Li, Hongbin Fang, Fan Feng, Paul Plucinsky, Richard James, Philip Buskohl, and Andrew Gillman.
Trisect an Angle with Origami. video by Numberphile.
When Math Met Origami. short talk by Robert Lang.
Mathematics Meets Origami. Erik Demaine, SIAM 2020.
Origami Simulator. Computational folding of stretchable origami (open source).
programming and computing
programming and computing
Probably the single most important takeaway from this (free) book can be summed up in the word: modular. It is (almost) always better to make a collection of separate small, simple things/tools/programs that are good at one specific task and link them together versus one big thing/tool/program which tries to do too much/everything.
This means interface design is important. Because you want to make connecting simple pieces easy.
julia. Programming language for scientific and general purpose computing.
git. Powerful and intuitive version control software.
Learn X in Y minutes. Get a crash course in almost any language, some development tools, and even some mathematics.
Coursera has more courses on computer science than I'm willing to list.
Algorithms
Introduction to Algorithms (MIT). Lecture series by Erik Demaine.
I found the dynamic programming lectures particularly helpful.
Richard Buckland (UNSW Sydney) has a few lectures series on YouTube that I recall enjoying:
Notes on Data Structures and Programming Techniques (Yale). Course notes.
P vs. NP. A nice, short introduction to the computational complexity classes and the P vs. NP problem.
D. Knuth. The Art of Computer Programming.
C/C++
Practical programming in C (MIT). Course notes, exercises, and answers to the exercises.
For anyone developing in C/C++: cmake and lldb.
There are many many many books on C++ that would I consider not very helpful (at best). However, Effective C++, More Effective C++, and Effective Modern C++ are books by Scott Meyers that are quite good.
Most Important Design Guideline. Talk by Scott Meyers.
Type Deduction and Why You Care. Talk by Scott Meyers.
Herb Sutter has some good C++ books as well.
Speaking of C++, Bjarne Stroustrup maintains a page with C++ resources. His book The C++ Programming Language is also a good resource. If I remember correctly, I learned most of what I know about templates from that book.
I haven't read it, but C++ Primer by Stanley B. Lippman, Josée Lajoie, and Barbara E. Moo is also supposed to be very good (and complete).
XSEDETraining. Videos and tutorials on a variety of topics related to high performance computing, machine learning, and scientific computing.
Lex Fridman. YouTube channel on a broad range of topics in STEM, but with a primary focus on artificial intelligence.
Microsoft Research. YouTube channel.
Computer Graphics. Lecture series by Keenan Crane.
Analog Computational Methods Workshop. Recording of a workshop on nontraditional computing organized by the Pittsburgh Quantum Institute.
Ben Eater. YouTube channel.
machine learning
machine learning
Intuition for machine learning. Lecture series by Cynthia Rudin.
One World Machine Learning. YouTube channel with recordings of research talks on machine learning. Top-notch seminar series.
AMMI Course "Geometric Deep Learning". A course on fundamental symmetry- and geometric-aspects of machine learning.
Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. Related paper/textbook.
Symmetry and Equivariance in Neural Networks. A nice talk by Tess Smidt on "symmetry-aware" machine learning.
Information theory, pattern recognition, and neural networks (Cambridge)
Aurélien Géron. YouTube channel on machine learning.
Machine learning on graphs. Lectures by Jure Leskovec (Stanford).
Graph Representation Learning. Book by Hamilton.
Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Recommended reading from the course.
Network science. Recommended reading for the course.
Stanford Network Analysis Project. Software package.
NetworkX. Another recommended software package.
offconvex. Blog by Sanjeev Arora.
Artificial Intelligence: A Guide for Thinking Humans. Very nice talk by Melanie Mitchell on some misconceptions and pitfalls in AI and ML.
Machine Learning TV. YouTube channel.
a bit of everything; misc.
a bit of everything; misc.
Quanta Magazine. A very nice resource for a concise, high-level view on a variety of topics. It is hard to read a lot of research articles, especially when they are on topics outside of your field(s) of expertise. Quanta is a nice way to stay up to date on some groundbreaking ideas and research being done in other fields. I really cannot recommend it enough.
How Mathematical ‘Hocus-Pocus’ Saved Particle Physics. Introduction to renormalization.
The ‘Useless’ Perspective That Transformed Mathematics. Introduction to representation theory.
GeoScience & GeoEnergy Webinars
Many good talks on flow through porous media; two of my favorite are...
Flow in porous materials: a tale of X-rays, minimal surfaces, and wettability. Talk by Martin Blunt.
Viscoelastic polymer flooding and flow instabilities in 3D porous media. Talk by Sujit Datta.
DNA origami
DNA origami: folded DNA as a building material for molecular devices. Talk by Paul Rothemund.
Nanofabrication via DNA Origami. Excellent talk on DNA origami by William Shih.
Part of the iBiology seminar series.
Ten years of DNA origami. Short overview by nature.
Applied Mechanics Reviews. Podcast-style interviews with great researchers and mechanicians.
imechanica. Forum for mechanics people to post new results, papers, talks, jobs, etc.
S. Yang and P. Sharma. A tutorial on the electrostatics of deformable materials with a focus on stability and bifurcation analysis.
Lanczos. The Variational Principles of Mechanics.
Gurtin, Fried, and Anand. The Mechanics and Thermodynamics of Continua.
There are many books on continuum mechanics, but this is probably my favorite. The section on kinematics, in particular, is very well done.
Rotations. An online resource from UC Berkeley on the mathematics of rotations. Many of the topics are supplemented by animations and the site provides MATLAB codes.
Efficient topology optimization in MATLAB using 88 lines of code.
TMP Chem. YouTube channel with a series of videos on physical chemistry.
Related: Symmetry Resources at Otterbein University. A nice collection of interactive and visual tools for understanding molecular symmetry.
Royal Institute. Excellent collection of technical talks.
International Centre for Theoretical Sciences. YouTube Channel with lectures on a variety of advanced topics in mathematics and physics.
International Centre for Theoretical Physics. YouTube Channel with lectures on a variety of advanced topics in mathematics and physics.
Kurzgesagt – In a Nutshell. YouTube channel.
Socratica. YouTube channel.
Domain of Science. YouTube channel.
Coursera. Has many freely available online courses; there are many in mathematics, physics, and computer science.
Class Central. A sort of search engine(?) for free online courses.
TheTrevTutor. YouTube channel. I found the two linguistics series to be particularly interesting. (It isn't easy to find a video series on linguistics!)
Khan Academy. Elementary (by design), but also remarkably clear. If you are totally new to a subject (or not so new but hoping to gain a nugget or two of added intuition), then this can be a great resource.
Primer. YouTube channel with some really interesting videos/simulations on natural selection and economics.
Veritasium. YouTube channel on some various STEM topics. I particularly enjoyed the Bayesian and origami videos.
Courses on Topology in Condensed Matter. YouTube Channel.
Intro. to Topological Mechanics. Lecture notes.
Princeton Center for Complex Materials. YouTube Channel.
Quantum mechanics
The Quantum Conspiracy (Ron Garret). A unique and (I think) important perspective on QM.
Operator mechanics: a new form of QM without matrices or waves. Very nice talk by Jim Freericks which is on a different way of approaching (and teaching) the fundamentals of QM.
Quantum Mechanics I (MIT). This entire lecture series is fantastic, but the first couple of lectures are especially good.
Quantum Mechanics (Stanford). Series of lectures by Leonard Susskind.
Understanding Quantum Entanglement. Talk by Philip Ball. I would recommend his work in general. He is quite good at making difficult concepts accessible.
Why Everything You Thought You Knew About Quantum Physics is Different. Philip Ball.
Entanglement and Complexity. Talk by L. Susskind.
Time
Why is Time a One-way Street. Talk by L. Susskind.
Free Will
Ben1994. "Anyone from anywhere can learn anything".
Page updated
Google Sites
Report abuse