Super, crazy, high-octante, MATHS
Maths allowing me to express my concepts on reality, otherworldly dimensions and black holes.
It’s a thing. A skill set I do not own. So, you may well ask- what maths are you in need of to hold the title, Theoretical Physicist?
There’s an online guide to the mathematics necessary in studying physics. I discovered it several months ago when pounding my head against a wall (figuratively) desiring a means to articulate my thoughts. It comes from Super String Theory and I clearly have a long way to go, but I am working on it!! 😉 Here’s the list to work through.
Calculus (single variable)
Ordinary Differential Equations & the Harmonic Oscillator (I do these all the time while riding my bike)
Partial Differential Equations
Methods of approximation
Probability and statistics
That’s not all! Then we have to work out- Real analysis (versus false, I suppose), Complex analysis, Group theory, Differential geometry, Lie groups, Differential forms, Homology, Cohomology, Homotopy (donut holes anyone?), Fiber bundles (not the ones your cat plays with!), Character classes, Index theorems, Supersymmetry and supergravity!
The mathematics behind supersymmetry apparently starts with two concepts: graded Lie algebras, and Grassmann numbers. A graded algebra is one that uses both commutation and anti-commutation relations. Grassmann numbers are anti-commuting numbers, so that x times y = –y times x. The mathematical technology needed to work in supersymmetry includes an understanding of graded Lie algebras, spinors in arbitrary spacetime dimensions, covariant derivatives of spinors, torsion, Killing spinors, and Grassmann multiplication, derivation and integration, and Kähler potentials. (excerpt from Superstringtheory’s website)
Noncommutative geometry- ok admittedly I first read, non-communicative and thought, I can totally relate to that! HA!
Meanwhile, I’m cutting out some Erwin Schrödinger snowflakes! Thank you, Symmetry Magazine!
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Andes Cruz: http://andescruz.wordpress.com
Kathleen Krucoff: http://kathleenkrucoff.wordpress.com/
Catherine Witherell: http://happydayart.typepad.com
Pallavi Gandhi: http://studioat605.wordpress.com/