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I'm new to Quantum dynamics as a whole and everytime i read an article on arxiv.org or watch a video on youtube and they introduce an equation like Shrodinger or other equations to show the logic and proof I find myself Banboozled and lost. Coming with no mathmatical backgroud I wanted to know if there are any resources out there with a curriculum that starts from the ground up, explaining all the math and mathematical expressions of quantum mechanics? If so please list them below.

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  • $\begingroup$ Depends on how much detail you want and what you want to study. If you want quantum mechanics ( physics side of things), you'll want to study linear algebra and differential equations. If you are more the quantum information and quantum computing you can replace differential equations with probability theory. This is just my opinion. Depending on what your math background is it can take quite some time if you want a deep understanding. $\endgroup$
    – Rammus
    Commented Jul 19, 2022 at 9:36
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    $\begingroup$ see physics.stackexchange.com/q/33215/58382. Though for most introductory books some degree of familiarity with basic calculus and linear algebra is assumed $\endgroup$
    – glS
    Commented Jul 19, 2022 at 9:38
  • $\begingroup$ If you plan to learn QC as a hobby then what others have suggested is a good route. If you want to do it somewhat professionally then you need at least an undergrad degree in STEM with decent math coursework. If you have STEM degree already then it should be relatively straightforward to understand basic ideas behind Schrodinger's equation, logic, probability etc. $\endgroup$
    – MonteNero
    Commented Jul 19, 2022 at 20:19

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Assuming that you have no background in single-variable calculus or linear algebra, I recommend you to start from such points. There are tons of material about this stuff online.

To know the basic tools of quantum computing you can try to get a place on QubitXQubit's Introduction to Quantum Computing course. There they cover all topics of quantum computing from the very start in a simple fashion (in fact, there are even many high-school students enrolled).

However, let me try to suggest you some material without "overloading" you.

In the case of Calculus, if you wish to be "practical", I recommend you Feynman's introductory book on problem-solving in physics. There he gives a brief explanation about derivatives and the basic tools that physicists mostly use and suggests some exercises. For a more complete treatment, the seminal textbook from James Stewart is a great start (this is actually the most used book in universities around the world.).

In the case of linear algebra, most quantum mechanics textbooks give a sufficient introduction in terms of the so-called Dirac notation, which is a notation invented by Paul Dirac, that facilitates a lot all the math-workout process for physicists. For a simple (but enough) treatment, see Griffith's textbook and for a more detailed explanation see Cohen's.

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