General
- Zoom Links (hybrid classes) מפגש זום
- Zoom Meetings (online classes) כלי/תוכן חיצוני (LTI)
יחידות הוראה
על הקורס - כללי
יחידות הוראה
Topics
"Computers are useless. They can only give you answers."
- Pablo Picasso
Lecture Zoom link
- Overview of general-purpose programming languages: Fortran, C, C++, Python
- Programing basics: variables, control flow, data objects, algorithms
- Overview of interpreted languages: Matlab, Mathematica
- Numerics: accuracy, precision, stability, bottlenecks, computer structure
- Numerical differentiation and integration; Runge Kutta methods
- Interpolation and extrapolation: polynomial, spline, Laplace
- Minimization and maximization: Brent, Newton, simulated annealing
- Statistical description of data: modeling, comparing distributions
- Monte Carlo simulations
- (Time permitting) Ordinary differential equations: finite differences, shooting, relaxation
- (Time permitting) Partial differential equations: reduction, relaxation, multi-grid
Lecture Topic Read Blank notes Class notes Links & extra 1 Course Intro, programming languages, C basics, random walk tutorials draft1 Lec1 Snake in 5 minutes; Dinosaurs in 3 minutes 2 Variable representation, precision, accuracy, loss of precision, recursion and differential equations NR1 draft2 Lec2
SnakeRoundoff disasters
One-liners 20103 Stability, scope of variables, arrays, passing variables by value/reference NR1 draft3 Lec3 C (de) referencing
scope4 Dynamical programming, continued fractions, interpolation and extrapolation: intro and Neville method, searching an ordered table, reading NR codes NR3 draft4 Lec4 Golden ratio
Interpolation in Python5 Interpolation: rational, spline, and multiple dimensions; Integration: Newton-Cotes formulae NR3 draft5 Lec5 Integration in Python 6 Newton-Cotes algorithms, Richardson extrapolation, Romberg open+closed methods, improper integrals 1 NR4 draft6 Lec6 P vs. NP 7 Improper integrals 2, orthogonal polynomials, Gaussian quadrature, integration in multiple dimensions NR4 draft7 Lec7 Monte Carlo examples 8 Statistics recap, Monte Carlo, MC examples, variance reduction, fractals, sampling from a distribution NR7.6-7.8draft8 Lec8 Mandelbrot zoom
Logistic map9 quasi-MC, importance+stratified sampling, diffusion with interactions, working with data, moments of a distribution 1 7.6-7.8
NR 14draft9 Lec9 Randomness 10 Pitfalls in statistics, moments of a distribution 2, estimating the significance of sample statistics, Student t-test, MC in statistics 1 NR14 draft10 Lec10 Simpson's paradox 11 Chi-squared test, MC in statistics 2, KS-test, MC simulation as an integral, Maximal likelihood NR14 draft11 Lec11 Lies, damn lies, and statistics 12 Chi-squared minimization, root finding: bracketing, bisection, secant, false position, Brent, Newton-Raphson NR15 draft12 Lec12 Hilbert to Turing
2D bracket13 Root finding in multiple dimensions: Newton-Raphson, Broyden; optimization: bracketing; ODEs: Euler, Runge-Kutta, explicit vs. implicit methods, stiff equations, adaptive step, Bulirsch-Stoer, shooting NR16 Textbooks
- Numerical recipes, by William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery; Publisher: Cambridge University Press; 3 edition (September 10, 2007).
- Computational physics, by Morten Hjorth Jensen; Publisher: CreateSpace Independent Publishing Platform (January 12, 2015)
- A survey of computational physics, by Rubin H. Landau, Jos? P?ez, Cristian C. Bordeianu; Publisher: Princeton University Press; Har/Cdr edition (July 21, 2008)
Lecture, Tutorial and office hours
Office Hours
Name Day Hours Building/Room Email* Uri Keshet Wed 17:00 Zoom ukeshet@bgu.ac.il David Uzan Thu 12:00 54/319 daviduz@post.bgu.ac.il Lecture/Tutorial
* Please use the course staff email only for private issues, material related issues should be addressed in the course forum.Group What? Name Day Hours Zoom/Hybrid 1 Lecture Uri Keshet Tue 14:10 - 17:00בניין כתות לימוד [35] חדר 213 11 Tutorial David Uzan Sun 18:10- 20:00 גולדברגר [28] חדר 202
Class Exercises
Recommendations
Tools:
- Lectures teach some C and Mathematica. Tutorials and assignments are in Python.
- Visual C, Python, Mathematica, and Matlab are installed on most BGU computers.
- Mathematica and Matlab are available within BGU campus and dorms on any mobile device through https://apps.bgu.ac.
il/ . - VPN to access the above - https://in.bgu.ac.il/computing/Pages/vpn-service.aspx ).
- We mainly run Python using Google Collab or Jupyter. A more professional IDE: PyCharm. Feel free to use any workspace convenient for you.
- C codes in this course are generally short, and can be compiled online e.g. on onlineGDB, ideone.com,
or codepad.org. - You may wish to compile C on your machine, which would be faster, much more powerful, and independent of web connection. You may need to install a compatible free compiler. For Windows, use command-line compilation (invoke "Command Prompt" from the start button). You may need to install Visual Studio first. A lighter alternative is MSYS2 installation.
- Before the course begins, we recommend refreshing your Python using some basic interactive guide (1, 2, 3, etc.), and becoming familiar with the Numpy, Scipy and Matplotlib libraries, which are used in the course.
- A C tutorial is also available and highly recommended.
- Euler Project is a nice project that has plenty of mathematical problems you could solve only by programming, and could help you learn coding in a more interesting way.
- Guido van Robot is a nice visual programming language that helps junior programmers understand the logic of coding. Recommended for students with no background in coding.
Course Policy
- A weekly lecture (3 hours) and a weekly tutorial (2 hours).
- A weekly problem set. Submit all (except maybe one) sets on time to attend the exam.
- Self-grade your problem set within a week after the solutions are posted; we will sample the grades. Final grade: 80% exam, 20% problem sets.