Many problems in visual computing, robotics, and mechanics lack exact analytical solutions. Numerical computing provides powerful techniques to approximate these solutions using computational methods, combining applied math and programming to solve real-world problems such as simulation, optimization, and data analysis. The course begins with a review on calculus and linear algebra, followed by an introduction to how numbers are represented on computers and error analysis. It then moves on to core topics, including matrix factorization, solving linear and nonlinear systems, optimization, and numerical solution of differential equations. Students will gain hands-on experience developing numerical algorithms and learn to balance accuracy, stability, and efficiency in problem-specific contexts, such as image processing, physics-based animation, motion planning and control, structural analysis, etc.
Acknowledgement: Lecture slides and written assignments are prepared based on materials from Solomon, J. (2015), Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics.
There will be 10 assignments, each covering two lectures and designed to be completed in less than 5 hours. Assignments include both written and programming components. Starter code (Python) will be provided.
Assignments are posted and submitted via Canvas, where grades will also be released. A1–A4 are due by Sunday at 23:59 of the corresponding week; starting from A5, each assignment is due by the following Monday at 15:29.
You have a total of 5 grace days for the semester, with a maximum of 2 grace days allowed per assignment. Each unused grace day will be 0.4% bonus points added to the final grades.
In this course, you are permitted to use generative AI tools for your assignments. These tools can be powerful aids for learning, debugging, exploring alternative explanations, improving clarity, and working more efficiently. Learning how to use them well is itself an important modern skill.
Use AI deliberately. Your goal should not be to outsource the homework, but to make thoughtful decisions about what you want to learn yourself and what you want to delegate to AI to save time. Exams are in class and allow only a letter-size cheat sheet, so AI tools will not be available there. The homework is therefore your main opportunity to build the understanding, judgment, and problem-solving fluency that you will need on exams.
Mandatory Appendix for AI Tool Usage. If you employ AI tools for your assignments, you are required to include an appendix in your submission that explains how and to what extent the AI tools were used. Briefly describe what you asked the tool to do, which parts of the final work were influenced by it, and what you verified or revised yourself.
Accuracy and Responsibility. AI-generated content may be incorrect, incomplete, or misleading. You are responsible for verifying the validity and relevance of anything you incorporate into your work, and for being able to explain your submitted solution. Failure to do so may result in a loss of scores.
By using AI tools in this course, you acknowledge your understanding and agreement to abide by these guidelines. Failure to comply will be considered a violation of CMU's academic integrity policy and may result in disciplinary actions.