MATH
21 B
Mathematics Math21b Spring 2017
Linear Algebra and Differential Equations
Linear algebra Math21b, Spring 2017
Course Head: Oliver Knill
Office: SciCtr 432
Mathematica projects are rolling in. Make sure the fitting works. Most errors appear there. Here is an example of a fitting plot. Make sure the bound for fitting is right. Here is a simple example:
data = {{1,2},{2,3},{3,5},{4,7},{5,11}};
f = Fit[data,{1, x, Log[x]}, x]
S1=ListPlot[data]; 
S2=Plot[f,{x,0,11},PlotStyle->Red];
Show[{S1,S2}]
The following three handouts cover the last part of the course The pendulum (animated below in Javascript) is simplified from a double pendulum. It is a periodically driven pendulum with friction x''=-sin(x)+ c x' + a sin(t) a system which is already chaotic in certain domains.
  • Mathematica project is posted. We have a workshop Wednesday, April 26, 2017, 6:00 PM - 7:00 PM in Hall C.
  • The hiring for Course Assistants for Math Ma, Mb, 1a, 1b, 21a, 21b, and 19b for the Fall/Spring 2017/2018 begins on April 13. Info sessions to field your questions about the hiring process or the job itself are on Tuesday, April 11 from 3:30-4pm in SC 216 and on Wednesday, April 12 from 3:30-4pm in SC 310. Having completed 21b you are eligible to apply to be a CA for Math Ma, Mb, 1a, 1b, 21a, 21b, 18, 19a and 19b. The application form is
    here.
    Then sign up for a micro-teaching
    here.
    Sessions will begin April 13 and continue over the next few weeks. Submit your application prior to signing up for your session. The main duties of the job involve attending section, grading homework, shifts at the MQC, and running problem sessions (or workshops in Ma, Mb and 1a). The hours per week are typically about 12-15 hours, never exceeding 20 hours. (Part time positions with fewer hours are also available). The compensation is 18 $/hour and 16.25$/hour for grading positions. Some former CAs have said that being a CA was one of their favorite parts of their undergraduate experience! If you have any questions, please contact Sarah Chisholm (chisholm@math.harvard.edu) or Yu-Wen Hsu (yuwenhsu@math.harvard.edu) or Neha Gupta (neha@math.harvard.edu).


    We are almost done with Math 21b. If you are thinking about future courses, the good news is that having done 21a and 21b essentially opens up all 100 level courses at the Math, the Stats and Applied Math departments. Also more physics, more advanced economics, computer science and chemistry courses will make sense with math 21a/b under the belt. In general, course choice is a highly personal matter. Advise which is good for one student might not be optimal for an other. Here are some examples to see what courses you could take later. The choice of examples is by no means a recommendation, nor does it mean that anything not mentioned should be avoided. Courses change from semester to semester and about matter of taste it is hard to advise "de gustibus non est disputandum" and there are always also new courses coming in or old courses disappear or change.
    Mathematics courses sample
    - Math 101 is an intro course to proofs
    - Math 112 real analysis "calculus with proofs". Can also serve as an intro to proofs)
    - Math 115 methods of analysis, useful for physics, requires Math 112.
    - Math 118 introduces dynamical systems no preknowledge in proofs required
    - Math 121 linear algebra with proofs, a more abstract, axiomatic approach
    - Math 122 theory of groups and vector spaces 
    - Math 135 differential geometry, develops calculus on curved spaces like surfaces
    - Math 152 discrete math, usually taught in a seminar format
    - Math 154 a basic introduction into probability theory
    - Math 155 combinatorics, counting techniques and methods in finite mathematics.
    - Math 157 Math in the world, no proofs, focus on problem solving 
    
    Statistics courses sample
    - Stat 110 Probability, a basic introduction into probability theory 
    - Stat 111 Theoretical statistics 
    - Stat 115 Computational biology and bioinformatics
    - Stat 121 Introduction to data science 
    - Stat 132 Applied quantitative finance
    - Stat 139 Statistical sleuthing through linear models
    - Stat 140 Design of experiments 
    - Stat 171 Introduction to Stochastic Processes
    
    Applied math courses sample
    - AM 104 does more Fourier stuff and lots more other things
    - AM 105 more differential equations both ODEs and PDEs.
    - AM 108 is nonlinear dynamical systems
    - AM 115 is modeling real-life phenomena
    - AM 120 applied linear algebra and big data
    - AM 121 optimization some Markov chains dynamical systems among other things
    - AM 158 feedback control systems geared towards engineering
    
    Computer Science courses sample
    - CS 20  Discrete Mathematics for Computer Science
    - CS 50  Introduction to Computer science 
    - CS 51  Introduction to Computer Science II 
    - SC 109 Introduction to Data Science
    - CS 121 Introduction to Computation
    - CS 124 Data Structures and Algorithms
    - CS 125 Algorithms and Complexity 
    - CS 127 Cryptography 
    - CS 134 Networks 
    
    Physics courses sample
    - Physics 15a  Mechanics Relativity
    - Physics 15b  Electromagnetism Stats
    - Physics 15c  Wave phenomena
    - Physics 16   Mechanics and relativity
    - Physics 143  Quantum mechanics
    - Physics 151  Mechanics
    - Physics 153  Electrodynamics
    - Physics 181  Statistical Mechanics and Thermodynamics
    - Physics 195  Solid state physics 
    
    Economics courses samples
    - Econ 1034 Networks 
    - Econ 1051 Introduction to Game theory
    - Econ 1123 Introduction to Econometrics
    - Econ 1126 Quantitative methods in Economics
    


    Please send questions and comments to knill@math.harvard.edu
    Math21b Harvard College Course ID:110989| Oliver Knill | Spring 2017 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas, for admin], Twitter