Contents

Syllabus

Syllabus

Course Information

  • Instructor(s): Kevin Vixie kvixie+589@wsu.edu

  • Course Assistants: TBA

  • Office: Neill 203

  • Office Hours: TBD

  • Course Homepage: Math Math (Spring 2022)

  • Class Number: 589

  • Title: Math 589: Topics in Analysis - Geometric Analysis with a View to Use

  • Credits: 3

  • Prerequisites: Linear Algebra

  • Meeting Time and Location: W, 1:10pm - 4pm, Terrell 106, Washington State University (WSU), Pullman, WA

  • Grading: Grade based on assignments and project presentation.

Textbooks

There is no formal textbook, but the following (available electronically from the WSU Library) will be useful:

[Gezerlis, 2020]

A. Gezerlis: “Numerical Methods in Physics with Python” (2020). This covers many useful algorithms with a focus on implementing them from scratch rather than using them as black-box routines.

[VanderPlas, 2016]

J. VanderPlas: “Python Data Science Handbook” (2016). More focused on data analysis, but Jake provides a very good description of techniques like plotting and animation. I have learned many of my skills from him and his blog Pythonic Perambulations.

Readings will be assigned as needed. See References for details and additional resources.

Student Learning Outcomes

The main objective of this course is for students to be able to effectively use numerical techniques to solve complex problems following principles of good software engineering and reproducible computing.

  1. Reproducible Computing: Write and communicate computational results in a way that allows one to reproduce these results in the future, possibly on different computing platforms.

  2. Problem Assessment: Be able to assess complex problems to determine if computational techniques will contribute to their solutions.

  3. Choice of Algorithm/Technique: Be able to identify which algorithms are appropriate for solving the computational problems.

  4. Implementation: Be able to implement the chosen algorithm.

  5. Convergence and Performance Analysis: Be able to quantify and understand the convergence and performance of the algorithm being used.

  6. Solution Assessment: Be able to assess the validity of the solution. For example, to quantify the uncertainties associated with the results, accounting for the accumulation of round-off, truncation, and discretization errors, with an understanding of the conditioning of both the problem and the algorithm.

  7. Communicate and Defend the Solution: Communicate the results with peers, defending the approximations made, the accuracy of the techniques used, and the assessment of the solutions. Demonstrate insight into the nature of the solutions, making appropriate generalizations, and providing intuitive descriptions of the quantitative behavior found from solving the problem.

These learning outcomes will be assessed through the assignments as follows:

  • By maintaining a code repository subject to automated testing, students will have to master all skills needed for reproducible computing (1).

  • Through the successful completion of their assignments, students will demonstrate the ability to choose a technique (3) and implement it (4).

  • Class assignments will test both accuracy and performance of the code. Passing the associated tests will require that students have understood the convergence and performance properties of there code (5).

  • Code coverage will ensure that students implement tests for their code, assessing their solutions (6).

  • Through code reviews and documentation, students will be required to communicate and defend their solutions (7).

Expectations for Student Effort

Students are expected to:

  1. Stay up to date with reading assignments.

  2. Participate in online forums, both asking questions and addressing peers questions.

  3. Identify areas of weakness, work with peers to understand difficult concepts, then present remaining areas of difficulty to the instructor for personal attention or for discussion in class.

  4. Complete assignments on time, providing well crafted solutions to the posed problems that demonstrate mastery of the material through the Learning Outcomes 1-7.

    Student’s are encouraged to discuss their intended approach with peers and with the instructor, but must ultimately write their own code.

For each hour of lecture equivalent, students should expect to have a minimum of two hours of work outside class.

Assessment and Grading Policy

Grading will be largely automated: you are expected to maintain a project on GitLab where you keep the code in a Git clone of the Official Course Repository. Your projects should contain all of the code you develop for this course, including solutions to the assignments. This code should be well-documented, and well-tested using GitLab’s continuous integration (CI) tools.

Each assignment will be distributed as a set of files made available through the main branch of the Official Course Repository: you will be instructed when to pull and merge these with your project. These assignments will contain skeleton code and tests. You will be expected to complete the skeleton code so that the tests pass.

These will include python code with skeleton functions, class, etc. which you are expected to complete, along with automated tests (which you must not modify) for the assignment, and CI instructions such that these tests can be run on GitLab, producing a badge for that assignment.

Your numeric grade for the course will be the percentage of passing assignment test badges for your code. Thus, if there are 10 assignments in the course and you have passing tests for 8 of those, you will have a grade of 80% to be converted to a letter grade according to the following table:

Percentage P

Grade

90% ≤ P

A

85% ≤ P < 90%

A-

80% ≤ P < 85%

B+

75% ≤ P < 80%

B

70% ≤ P < 75%

B-

65% ≤ P < 70%

C+

60% ≤ P < 65%

C

55% ≤ P < 60%

C-

50% ≤ P < 55%

D+

40% ≤ P < 50%

D

P < 40%

F

There will be no exams in this course.

Attendance and Make-up Policy

While there is no strict attendance policy, students are expected attend an participate in classroom activities and discussion. Students who miss class are expected to cover the missed material on their own, e.g. by borrowing their classmates notes, reviewing recorded lectures (if available), etc.

Course Timeline

  1. Introduction and Basic Principles (~2-3 week)

    • Structure of the course.

    • Establish accounts and appropriate projects on CoCalc and GitLab

    • Numerical Evaluation of functions: Round-off error etc. (Assignment 0).

    • The Monty Hall Problem: Simple Monte Carlo Analysis (Assignment 1).

  2. Basic Techniques (~2-3 weeks)

    • Differentiation and Integration.

    • Optimization and Root Finding.

    • Interpolation: Splines, Polynomials, Radial Basis Functions (RBF), Gaussian Processes.

    • Loops, Arrays, etc.

    • Bases.

  3. Curve Fitting/Cycle Finding (~2 week)

    • Finding cycles in data.

    • Least squares fitting.

    • Fourier analysis.

    • Other techniques.

    • Bayesian techniques.

  4. Ordinary Differential Equations (ODEs) (~1-2 week)

    • Orbiting Planets.

    • Falling Objects.

    • Agent-Based Modeling.

  5. Partial Differential Equations (PDFs) (~2 weeks)

    • Schrodinger Equation

    • Fluid Dynamics

    • Diffusion

  6. Other Topics/Domain Specific Problems (~4-6 weeks)

    • Renormalization Group, Effective Theories

    • Cellular Automata

    • Domain specific problems designed to address challenging problems in the fields of study represented by participants in the class.

    • Visualization techniques.

    • Profiling and Optimization.

Exact topics and techniques will be chosen to match the interests and needs of the participants (who are expected to communicate these needs to the instructor in advance of the course), but may include:

  • Case-studies: Part of the course will explore real-world examples of how physics has inspired solutions to hard problems in other fields of study.

  • Root-finding and Optimization

    • Finding ground states and excited states in quantum mechanics.

    • Density Functional Theory (DFT)

    • Machine learning (Probably not in the first year…)

  • Reaction/Diffusion networks:

  • Ordinary Differential equations and Boundary Value Problems:

    • Classical Mechanics

    • Classical Chaos

    • Time-dependent Schrödinger equation.

  • Partial Differential Equations

    • Time-dependent Schrödinger equation/Time-dependent DFT (TDDFT)

    • Fluid dynamics (Continuing from Matt’s course).

      • Simple parallization: what to do when your data does not fit on a single node. (@m.duez)

    • Numerical Relativity (Probably not in the first year…)

    • Finite element techniques + Green’s Functions for wave dynamics (Talk to Phil).

  • Monte Carlo

    • Simulation of thermodynamic systems

    • Numerical experiments with Renormalization Group

    • Quantum Monte Carlo (QMC) (Probably not in the first year…)

  • Bayesian Analysis

    • Linear and Non-linear model fitting which properly characterized errors.

    • Manifold reduction techniques.

  • Data Analysis

    • How to access, store, and analyze data.

    • Clustering and searching in high dimensions. (@gworthey)

Reading Schedule

The following details the content of the course. It essentially follows the main textbook. Content from the supplement will be inserted as appropriate throughout.

See References.

Other Information

COVID-19 Statement

Per the proclamation of Governor Inslee on August 18, 2021, masks that cover both the nose and mouth must be worn by all people over the age of five while indoors in public spaces. This includes all WSU owned and operated facilities. The state-wide mask mandate goes into effect on Monday, August 23, 2021, and will be effective until further notice.

Public health directives may be adjusted throughout the year to respond to the evolving COVID-19 pandemic. Directives may include, but are not limited to, compliance with WSU’s COVID-19 vaccination policy, wearing a cloth face covering, physically distancing, and sanitizing common-use spaces. All current COVID-19 related university policies and public health directives are located at https://wsu.edu/covid-19/. Students who choose not to comply with these directives may be required to leave the classroom; in egregious or repetitive cases, student non-compliance may be referred to the Center for Community Standards for action under the Standards of Conduct for Students.

Academic Integrity

Academic integrity is the cornerstone of higher education. As such, all members of the university community share responsibility for maintaining and promoting the principles of integrity in all activities, including academic integrity and honest scholarship. Academic integrity will be strongly enforced in this course. Students who violate WSU’s Academic Integrity Policy (identified in Washington Administrative Code (WAC) WAC 504-26-010(3) and -404) will fail the course, will not have the option to withdraw from the course pending an appeal, and will be Graduate: 6300, 26300 reported to the Office of Student Conduct.

Cheating includes, but is not limited to, plagiarism and unauthorized collaboration as defined in the Standards of Conduct for Students, WAC 504-26-010(3). You need to read and understand all of the definitions of cheating. If you have any questions about what is and is not allowed in this course, you should ask course instructors before proceeding.

If you wish to appeal a faculty member’s decision relating to academic integrity, please use the form available at _communitystandards.wsu.edu. Make sure you submit your appeal within 21 calendar days of the faculty member’s decision.

Academic dishonesty, including all forms of cheating, plagiarism, and fabrication, is prohibited. Violations of the academic standards for the lecture or lab, or the Washington Administrative Code on academic integrity

Students with Disabilities

Reasonable accommodations are available for students with a documented disability. If you have a disability and need accommodations to fully participate in this class, please either visit or call the Access Center at (Washington Building 217, Phone: 509-335-3417, E-mail: mailto:Access.Center@wsu.edu, URL: https://accesscenter.wsu.edu) to schedule an appointment with an Access Advisor. All accommodations MUST be approved through the Access Center. For more information contact a Disability Specialist on your home campus.

Campus Safety

Classroom and campus safety are of paramount importance at Washington State University, and are the shared responsibility of the entire campus population. WSU urges students to follow the “Alert, Assess, Act,” protocol for all types of emergencies and the “Run, Hide, Fight” response for an active shooter incident. Remain ALERT (through direct observation or emergency notification), ASSESS your specific situation, and ACT in the most appropriate way to assure your own safety (and the safety of others if you are able).

Please sign up for emergency alerts on your account at MyWSU. For more information on this subject, campus safety, and related topics, please view the FBI’s Run, Hide, Fight video and visit the WSU safety portal.

Students in Crisis - Pullman Resources

If you or someone you know is in immediate danger, DIAL 911 FIRST!

  • Student Care Network: https://studentcare.wsu.edu/

  • Cougar Transit: 978 267-7233

  • WSU Counseling and Psychological Services (CAPS): 509 335-2159

  • Suicide Prevention Hotline: 800 273-8255

  • Crisis Text Line: Text HOME to 741741

  • WSU Police: 509 335-8548

  • Pullman Police (Non-Emergency): 509 332-2521

  • WSU Office of Civil Rights Compliance & Investigation: 509 335-8288

  • Alternatives to Violence on the Palouse: 877 334-2887

  • Pullman 24-Hour Crisis Line: 509 334-1133

previous

Lecture 4: Derivatives are Local Approximations

next

Readings