What Were the Hardest Math Subjects When Starting Physics as a Bachelor Student?

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Struggling with advanced mathematics, particularly infinite series and their tests like the Integral Test, is a common challenge for recent physics graduates. Mastery of a few key mathematical tricks can significantly impact grades, with a small set of techniques often leading to better understanding and performance. Important topics to focus on include power series, complex numbers, linear equations, and Fourier series, as they provide foundational insights. Differential equations also require attention to fundamental concepts despite having numerous tricks. For effective problem-solving practice, resources like the Schaum's Outline series are recommended. Specific techniques, such as integrating with respect to y before x in double integrals and strategic row operations in matrices, can simplify complex problems. Additionally, understanding Euler's formula enhances comprehension of trigonometric relationships, illustrating the interconnectedness of mathematical concepts.
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I'm a recent bachelor student into physics and I am really struggling with these type of maths. Especially infinite series and its tests, the Integral Test and etc. If it was easy for you, what type of books did you use or methods?
 
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A lot of undergraduate math subjects have a small set of tricks. If you learn 3, you get a C, learn 5 and you get a B, learn 7 and you get an A. You must survive that, but often those tricks do not give you great insight. Keep your eyes open for the exceptions: power series and complex numbers, linear equations, fourier series, etc. Those are the subjects that you really want to take to heart. The subject of differential equations has a dozen tricks, but the basics are really fundamental. You can tell that if there is an entire math class on a subject, then you will see a bit of it in the early classes that you should pay special attention to.
For practice in solving problems, I always recommend the Schaum's Outline series.
 
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The one trick among many that i still recall was integrating y first before x in a double integral.

The prof mentioned it in passing and then on the surprise quiz he had such an integral impossible to integrate starting with x first but a piece of cake when starting with y.

Another was from Linear Algebra, in adding and subtracting rows in a matrix to get a 1 value in a column over dividing the selected row by the inverse of the column number.

More recently, I learned that Euler's formula could be used to derive the sin/cos relationships for adding and subtracting angles.
 
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I graduated with a BSc in Physics in 2020. Since there were limited opportunities in my country (mostly teaching), I decided to improve my programming skills and began working in IT, first as a software engineer and later as a quality assurance engineer, where I’ve now spent about 3 years. While this career path has provided financial stability, I’ve realized that my excitement and passion aren’t really there, unlike what I felt when studying or doing research in physics. Working in IT...
I have a specialization in condensed matter physics and materials physics, and off-late, I have been seeing a lot of research directions moving towards quantum computing (AMO and non-linear optics) and the huge chunk of quantum materials research (and funding) is dedicated towards QIS and QC research. I am wondering (sort of in a dilemma), if I should consider switching my field? I am currently at the stage of a postdoc.

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