Know any other great mathematical physics textbooks? Please share in the comments.

**1. Mathematical Methods for Physics and Engineering by Riley, Hobson and Bence**

One of the classic basic mathematical physics books. This 1359 page tome offers an in depth analysis of all the basic topics as well as over 800 exercises. In particular, the book starts off with basic algebra and calculus, as well as a great introduction to series and complex functions. More advanced and specialized topics, such as quantum operators, probability theory and statistics are covered as well. The book offers a great introduction and a reference guide for later undergrad years. The only con of this book in my eyes is the annoying student solution manual that has to be bought separately. Selling the solution manuals separately, unfortunately, seems to be a vice shared by many of similar textbooks.

**2. A Course of Modern Mathematical Physics by Szekeres**

This course on mathematical physics by Szekeres has a reputation of being a quick, yet an in-depth overview of the core concepts of mathematical physics. One obvious advantage is the “tiny” size of the book — being more than twice as short as the book in the previous entry, *A Course of Modern Mathematical *covers roughly the same material.

**3. Mathematical Methods in the Physical Sciences by Boas **

Here we have another classic textbook. Written by Mary L. Boas back in 1966, the 3d edition of the book still dominates the shelves and happens to be one of the popular reference guides to both math and physics undergrads. The topics covered include basic algebra, calculus, complex analysis, series, differential equations, statistics and probability theory, tensors and a few others. In addition, the book contains problems after each section with answers to selected problems given at the end.

**4. Mathematical Methods for Physicists by Arfken, Weber and Harris **

Another popular textbook often used as a reference source in many mathematical physics courses. Even though the book is widely used among undergrads, the reviews range from awful to absolutely recommended. Common complaints of the book focus on the lack of solutions to the exercises and the lack of depth in certain chapters. On the positive note, the book is often regarded as one of the best sources for refreshing your mathematical physics knowledge.

**5. Mathematical Techniques by Jordan and Smith**

This entry has a reputation for being an easily accessible, clear and no-nonsense guide to mathematical techniques for physicists and engineers. The topic selection is a bit smaller than in the previous entries, but all the crucial topics are still there. In addition to the problems at the end of each section, the reader is also offered a selection of self-check questions.

**Bonus: Mathematics for Physics by Stone and Goldbart**

Here we have a free pre-publication pdf version of the great textbook by Stone and Goldbart. It is geared towards graduate students and thus covers a little more advanced topics, including complex analysis, lie groups, calculus of manifolds, geometry of fibre bundles and so on.

]]>** Winter is Coming **by Kostov and Allan

It’s not a secret that scientists often turn out to be quite geeky. Whether it’s memorizing countless digits of pi or Dungeons and Dragons, everyone chooses their own poison. This paper, however, even by the geek standards goes too far. Veselin Kostov and Daniel Allan aim to predict the rather erratic climate changes in the world of *The Song of Fire and Ice *by doing some tricky three-body dynamics. Is it a serious paper? You tell me.

* The Socceral Force *by Batfai

The author apparently has an audacious dream of creating a virtual reality system to support the decision making in European football. This paper is the practical manifestation of this dream.

* Ham Sandwich with Mayo *by Elton and Hill

I’ll be honest with you, I have no idea what the *classical ham sandwich theorem of Banach and Steinhaus *is, but we need more paper titles like this.

* Holly Balls! *by Wright, Langley, Belden & Truscott

Having a paper with a title like this in one’s publication list is equivalent to having your email address listed as 2stoned2care@penisland.net on your CV. And yes, in case you’re wondering, it’s a real domain name. Oh, and the paper is about ball behavior on water surface.

You think the title is bad? Check out the abstract. P.s. arXiv doesn’t display the abstract, so had to use another link.

* Would Bohr be born if Bohm were born before Born? *by Nikolic

This one actually seems like a really interesting paper.

]]>The Theoretical Minimum website includes 6 main lecture courses, plus additional 9 courses on advanced topics. The archive section contains older versions of the core courses. Here’s the list of topics covered in core courses:

1.** Classical Mechanics** (Newton’s laws, Lagrangian, electromagnetic fields, symmetries and conversations)

2. **Quantum Mechanics** (vector spaces, Schrodinger’s equation, entanglement, Fourier analysis, particles)

3. **Special Relativity and Electrodynamics **(Lorentz transformations, velocity addition, classical field theory, Maxwell equations)

4. **General Relativity** (equivalence principle, tensors, curvature, geodesics, black holes, field equations, gravity waves)

5. **Cosmology** (expanding universe, curvature, cosmic thermodynamics, baryogenesis, inflation, quantum fluctuations)

6. **Statistical physics** (entropy, temperature, Boltzmann distribution, reversibility, liquid-gas transition)

For more high-quality lectures visit Stanford University **YouTube channel**.

Many of Einstein’s works and books can be found in the public domain. This **page** contains 9 files with different works of Einstein, such as *Relativity: The Special and General Theory, The World as I see It *and his other works on science, worldview, politics and religion. This **page** also contains some interesting documents from the *National Academy of Sciences* related to Einstein. Another great collection of documents and other related stuff comes from *Leo Baeck Institute Archives *and can be found **here**. It includes some interesting historic documents, such as Eisntein’s letters to Roosevelt, the Queen Elizabeth of Belgium and other great stuff.

The public domain is also home for rare original video footage. In this rare footage below we can see Albert Einstein arriving to US after fleeing the Nazi Germany in 1933. More cool footage can be found by using the search function at **archive.com**.

**10. Why Are We Happy? Why Aren’t We Happy?**

In this talk Dan Gilbert, the author of *Stumbling on Happiness*, challenges the idea that we’ll be miserable if we don’t get what we want. According to Gilbert, there are many surprising ways to reach happiness, even if everything doesn’t go as expected. So what is the secret of happiness? Dan Gilbert might have an answer.

**9. Unveiling Game-Changing Wearable Tech**

In this talk Pattie Maes presents some breakthrough wearable inventions that have the potential to change the world. This includes a wearable device with a projector that paves the way for profound interaction with our environment and other cool demos. For more info visit this **link**.

**8. How Simple Ideas Lead to Scientific Discoveries**

Adam Savage walks through two spectacular examples of profound scientific discoveries that came from simple, creative methods anyone could have followed — Eratosthenes’ calculation of the Earth’s circumference around 200 BC and Hippolyte Fizeau’s measurement of the speed of light in 1849.

**7. Conception to Birth**

Alexander Tsiaras is an image-maker and in this fascinating TED talk he will share a powerful medical visualization, showing human development from conception to birth and beyond. Breath-taking images combined with some amazing music tells the story of the beginning of a human being.

**6. The Paradox of Choice**

In one of the most popular TED talks Barry Schwartz presents his ideas on the central tenet of western societies: freedom of choice. This paradox of choice, according to Barry Schwarz, can be seen in economics, psychology, healthcare and the lifestyle of Americans. What is this paradox of choice? Find out in this great TED talk.

**5. Thrilling Potential of SixthSense Technology**

This popular talk from TEDIndia introduces the amazing *SixthSense* devices, which connect the world of data with the physical world. The demonstration also includes the paradigm-shifting paper laptop & other innovative inventions that have the potential to change the world.

**4 . The Astounding Athletic Power of Quadcopters **

What’s a quadcopter? Well, it’s an agile flying robot that can solve physical problems by using special algorithms that allow them to learn. In this demonstration Raffaello D’Andrea demonstrates how quads work and why they are amazing.

**3. The Puzzle of Motivation**

What is the answer to the puzzle of motivation? Dan Pink thinks he knows the answer. And that surprising answer comes from the social scientists rather than managers. Traditional rewards, as Pink explains, aren’t always as effective as we think. That leads to the answer of what is the best way to motivate people, which is discussed in this talk.

**2. Stephen Hawking: Questioning the Universe**

In this popular TED talk Stephen Hawking himself delivers a presentation to the TED audience. This talk is all about questions. Questions that are as big as the universe. How did the universe begin? How did life begin? What will be the fate of the universe? These and other great questions are pondered by the great scientist.

**1. Do Schools Kill Creativity?**

In this talk, which is currently the most watched TED talk in the given category, Sir Ken Robinson, an author, speaker and an educationalist, presents his ideas on how to bring the system of education to the 21st century. The key of successful education system, according to Robinson, is the nurturing of creativity — the pillar of all great inventions.

]]>**Archaeology****Architecture****Atoms****Brain****Earth’s Crust****Earth’s Seasons****Electricity****Energy****Eyeballs****Flight****Forensics****Genes****Gravity****Light Optics, Bending and Bouncing****Magnetism****Motion****Patterns****Phases of Matter****Planets and Moons****Plants****Pollution Solutions****Probability****Simple Machines****Spiders****Spinning Things****Static Electricity****The Moon****Time****Water Cycle****Waves**

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1. *University Physics with Modern Physics* by Young, Freedman & Lewis Ford

*University Physics *is one of the most popular physics textbooks used in many universities around the world. This beast of a book (1600 pages) covers all the basics that a physics or engineering student might need, plus adds a thorough introduction to modern physics. The topics covered include: mechanics, thermodynamics, waves, optics & modern physics. The modern physics section covers relativity, quantum mechanics, particle physics, cosmology & atomic structure. Due to the relatively high price of the 13th edition, many students might prefer the 12th edition, which covers mostly the same topics.

2. *Physics for Scientists and Engineers with Modern Physics *by Douglas C. Giancoli

This one is another popular textbook focusing on the basics of physics for university students. The book is a little shorter and cheaper than *University Physics, *however it covers almost the exact same topics. The textbook has a nice structure, with an emphasis on examples. In addition, it is calculus based, which is pretty standard for many of similar textbooks, however, this book seems to have the right level of difficulty. For students from other disciplines, or simply those, who are looking for something lighter in terms of math, there is a very nice algebraic introductory textbook by Giancoli called *Physics: Principles and Applications. * This text is cheaper and is dedicated to pre-med, agricultural, technology, and architectural students.

3. **Fundamentals of Physics ****by David Halliday, Robert Resnick and Jearl Walker**

Here we have another classic textbook, which is often regarded as *the gold standard *of freshman textbooks and also happens to be my personal favourite. What is more, in 2002, *Fundamentals of Physics *was named the most outstanding introductory physics textbook of the 20th century by the American Physical Society. Like other books from this list, *Fundamentals of Physics* is a huge tome that covers all the major areas of undergraduate physics. In particular, the main topics include: basics of physics and mechanics, waves, electromagnetism, thermodynamics, optics and special relativity. The extended edition of the textbook also covers such modern physics topics as quantum mechanics, solid state physics, atomic and molecular physics and cosmology. Two great features of the book, that I found especially helpful, were the sample problems for each topic and the summaries after each chapter, which were invaluable during exam revision. In addition to that, *Fundamental of Physics *has plenty of problems after each chapter, which are also a great source for extra practice.

4. *Physics for Scientists and Engineers: A Strategic Approach* by Randall D. Knight

*Physics for Scientists and Engineers *is another widely acclaimed textbook used in physics classes all around the world. The author has a reputation of using as little math as possible and focusing on the logic of problem solving, which you may like or hate depending on what you want to learn. The book is often mentioned among the textbooks that focus on educational research to update and improve the material with each new edition. This is obvious in the new edition, which has additional chapter previews, challenge examples, problem sets and summaries.

5. *The Feynman Lectures on Physics* by Richard Feynman

*The Feynman Lectures on Physics *are often regarded as one of the most popular physics textbooks ever written. And while it is hard to say if that is true or not, one thing is undeniable — these lectures are invaluable when it comes to teaching conceptual understanding of basic physics. Most people, including experts of the field, recommend *The Feynman Lectures *due to their intuitive explanation of complex topics and an original approach to teaching undergrad physics. One disadvantage of these books, however, is a lack of focus on problem solving, which is obviously a major part of any physics course. Despite that, most physicists would likely agree that anyone with an interest in physics should read these books at least once.

Agree, disagree? Have your own favourite textbook? Please share in the comment section below.

**Extra links:**

**A free physics textbook: Motion Mountain**

All of these papers are undeniably great, since they introduced revolutionary theoretical ideas, that often turned a new page in the history of physics. However, a paper does not require a “revolution” to be considered influential and highly useful. Many great papers carve their mark in the history of physics through silence ingenuity. And today, through the wonders of online databases, it is easier than ever to track the top papers and their citations. So I thought it would be a good idea to do some research and find out what are the currently mostly cited research papers. Below you can find 2 lists of currently most cited papers and an additional list with the most cited papers of the last 110 years.

Now it is important to point out that, given the number scientific journals and the difficulty of tracking the citations of old papers, it is nearly impossible to find an absolutely accurate list of top papers. Despite these drawbacks, however, there are some reliable databases that track the number of citations for each paper. Among these we can find such sources as the Inspire HEP database, Google scholar and **this** great paper on the most cited Physical review papers throughout the last hundred years. The top 10 papers from each source are given below.

The first source, Inspire HEP, is an open access digital library for the field of high energy physics. It has been the main research paper database on the subject since 1970s. Each year Inspire publishes lists of top cited papers, both of that year and all time. Here are the top 10 papers of the year 2013.

Google Scholar is a more recent database, or, more correctly, a search engine dedicated to scientific research papers. One of the best features of the Scholar is a rating system that tracks the most cited papers for each category. Here are the 10 top cited physics & math papers from Physical Review Letters.

Last, but not least, we have 10 leading papers from the 110 years of research, as seen on Physical Review journals. In this **paper** S. Redner analyzes the most impactful and highly cited historic papers. Here are the 10 papers (actually it’s 11, since there seems to be a tie between two of the papers) rated according their number of cites. For some other interesting data, check out the original paper.

# |
Title |
Author(s) |

1. | Self-Consistent Equations Including Exchange and Correlation Effects (1965) |
W. Kohn, L. J. Sham |

2. | Inhomogeneous Electron Gas (1964) |
P. Honenberg, W. Kohn |

3. | Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems (1981) |
J.P. Perdew, Alex Zunger |

4. | Ground State of the Electron Gas by a Stochastic Method (1980) |
D. M. Ceperley, B.J. Alder |

5. | Theory of Superconductivity (1957) |
J. Bardeen, L.N. Cooper, J.R. Schrieffer |

6. | Model of Leptons (1967) |
S. Weinberg |

7. | Linear Methods in Band Theory (1975) |
O. K. Andersen |

8. | Effects of Configuration Interaction on Intensities and Phase Shifts (1961) |
U. Fano |

8. | Disordered Electronic Systems (1985) |
P.A. Lee, T.V. Ramakrishnan |

9. | The Electronic Properties of Two-Dimensional Systems (1982) |
T. Ando, A.B. Fowler, F. Stern |

10. | Special Points for Brilloun-Zone Integrations (1976) |
H.J. Monkhorst, James D. Pack |

**Links:**

**HEP database**

**Google Scholar top cited papers**

**Top cited papers of last 110 years **