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Lecture 2: The taxonomy of numbers: P,N,Z,Q,F,I,R,C Numerical taxonomy: Applications of integers Exercises NS Lecture 3: (Week 2) The role of physics in mathematics The three streams in mathematics Stream : Prime number theorems Stream 2: Fundamental theorem of algebra Stream 3: Fundamental theorems of calculus Other key theorems in mathematics Lecture 4: (Week 3) Applications of Prime number Lecture : The Euclidean algorithm (GCD) Exercises NS Lecture 6: Continued fractions Lecture 7: Pythagorean triplets (Euclid s formula) Lecture 8: Pell s equation Lecture 9: Fibonacci sequence Exercises NS Stream 2: Algebraic Equations (2 Lectures) Lecture 0: Algebra and geometry as physics The first algebra Finding roots of polynomials Matrix formulation of the polynomial Working with polynomials in Matlab/Octave: Lecture : (Week 4) Eigenanalysis Eigenvalues of a matrix Taylor series Analytic functions: Complex analytic functions:Ĥ 4 CONTENTS 3.3 Exercises AE Lecture 2: (Week ) Root classification Convolution of monomials Residue expansions of rational functions Lecture 3: Introduction to Analytic Geometry Development of Analytic Geometry Lecture 4: Applications of scalar products Lecture : (Week 6) Gaussian Elimination Exercises AE Lecture 6: Transmission (ABCD) matrix composition method Thévenin transfer impedance Lecture 7: Impedance matrix Lecture 8: Power relations and impedance Power vs. Early science and mathematics Lecture : (Week ) Three Streams from the Pythagorean theorem What is science? What is mathematics? Early physics as mathematics Modern mathematics is born Science meets mathematics The Three Pythagorean Streams Stream : Number Systems (9 Lectures) 2 2. Allen Copyright 206,7,8,9 Jont Allen University of Illinois at Urbana-Champaign Thursday 6 th June, :33 Version cģ Contents Introduction 3.
1 An Invitation to Mathematical Physics and Its History Jont B.
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