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I know there are a lot of resources available out there for learning Wolfram Language. However, I would like to create a specific query here (which might lead to a useful thread in the future). I would be soon starting a PhD in String Theory and would like to learn Mathematica to make my life easy. Hence, I am looking for resources that I can use to learn Mathematica that I would be using in string theory research. As of what I know right now, there are three broad classifications of the tasks that a Theoretical physicist would be undertaking,

  1. Complicated algebraic tasks, which may involve vectors, tensors etc and their manipulations. This may also involve tasks like using differential operators, differntial forms and all sorts of algebras like lie algebra, supersymmetric algebra etc.

  2. The numerical solution to things like eigenvalue problems, differential equations both ordinary and partial etc, which may involve use of several data structures like lists and tables.

  3. Simulation and/or data analysis and visualization (plots etc).

I know no single book would teach all the three sorts. But can someone recommend books, resources, courses etc for each type or something? Please feel free to add to the list if I have missed a particular classification.

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    $\begingroup$ Wolfram Physics Project, Peter Woit's - Not Even Wrong, Sabine Hossenfelder's- Lost in Math: How Beauty Leads Physics Astray, just my first thoughts. The Wolfram site shows lots of applications of Mathematica for theoretical physics, the other links show some of the traps that can derail analysis and thought. $\endgroup$
    – Jagra
    Dec 24, 2020 at 14:30
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    $\begingroup$ Not certain why someone would vote to close this question. The OP has asked for "resources",something this site has always encouraged. Note, the OP has not asked for "opinions" about the respective value of such resources. This seems a fair and interesting question. $\endgroup$
    – Jagra
    Dec 24, 2020 at 14:58

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I have written a book on Using Mathematica for Quantum Mechanics (A Student's Manual) that you can buy on Amazon. It contains much material on vectors, matrices, tensors, tensor construction, eigenvalue problems, simulations, etc. No string theory, just plain quantum mechanics with spins and in real-space (and combinations of the two).

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  • $\begingroup$ Wow! That is fantastic! Thanks a lot. I will definitely do that! $\endgroup$ Feb 10, 2021 at 17:22
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Take a look at the website for the Mathematica Summer School on Theoretical Physics. It contains all the resources, slides, notebooks, exercises etc for the past summer schools. The topics are always in cutting edge of theoretical physics (Holographics Entanglement Entropy and Tensor Networks, Integrability and Super Yang-Mills theories, Scattering Amplitudes and AdS/CFT etc.).

The 9th edition was supposed to be held in 2020, but was postponed due to the COVID-19 situation. I can highly recommend you to talk to your supervisor and signup for the next summer school as you will gain a lot from it.

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