2013 is about to pass, and my sophomore year is also nearly half over. This semester, I have been much busier with matters at the radio station, and my progress in mathematics and physics has been slightly slower than expected. The main advancements have been in vector analysis (field theory), path integrals, and differential equations.
Next semester, specialization selection begins. I have chosen the non-teaching track, although in reality, I prefer the courses in the teaching track. The only reason I chose the non-teaching track is that the teaching track requires taking Education and Psychology. Fortunately, our Innovation Class offers a lot of freedom, allowing us to freely choose courses for the next semester. I have selected six mathematics courses:
1. Ordinary Differential Equations;
2. Functions of a Complex Variable;
(These two are purely for earning credits; I feel I already understand what will be taught, while the parts I consider important won’t be covered...)
3. Mathematical Statistics;
(The main idea for this course is to lay the foundation for path integrals and statistical mechanics)
4. Differential Geometry;
(Mainly as a foundation for General Relativity and the formalisms of theoretical physics)
5. Partial Differential Equations;
(Both 4 and 5 are junior-year courses; I will be taking them with the juniors)
6. Discrete Mathematics.
Goals for the next semester:
1. Learn to draw Feynman diagrams. This goal naturally includes advanced Quantum Mechanics and an introduction to Quantum Field Theory (I am determined to immerse myself in the path integral formulation);
2. Intensively read Tristan Needham’s Visual Complex Analysis, becoming proficient in combining complex variables and differential geometry;
3. Closely read Hilbert’s Geometry and the Imagination;
4. Regarding differential equations, strive to become more proficient in Lie symmetry methods for differential equations;
5. If possible, read some Econophysics and Quantum Finance.
I wonder how many of these goals will be achieved? In 2014, I wish everyone all the best.
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