Definition of battery Working mechanism History of batteries Technology development Important types of batteries Characteristics, Comparisons
Section 1 Introduction of energy on the earth Section II Fundamentals of Fuel Cell Chemical power sources Section III Fundamentals of Solar Cell Physical power sources
1 Linear Algebra Notations and Fundamental Concepts Matrix Multiplication Operational Properties Linear Space Quadratic Form and Positive Definite Matrix Matrix Calculus 2 Probability Theory Probability Space Random Variable and Its Distribution Numerical Characteristics of Random Variables Conditional Expectation Jenson’s Inequality
Number Theory 1. Six proofs of the infinity of primes …… 3. Binomial coefficients are (almost) never powers 4. Representing numbers as sums of two squares …… 8. Some irrational numbers 9. Three times π2/6 Geometry 10. Hilbert’s third problem: decomposing polyhedra63 11. Lines in the plane and decompositions of graphs …… 15. The Borromean rings don’t exist …… 17. Every large point set has an obtuse angle 18. Borsuk’s conjecture Analysis …… 21. The fundamental theorem of algebra …… 25. Cotangent and the Herglotz trick 26. Buffon’s needle problem Combinatorics 27. Pigeon-hole and double counting …… 32. Cayley’s formula for the number of trees 33. Identities versus bijections …… 36. The Dinitz problem247 37. Permanents and the power of entropy253 …… 41. Communicating without errors 42. The chromatic number of Kneser graphs …… 44. Probability makes counting (sometimes) easy