# 6-23-25 ## Action Items - Reserve the classroom for office hours from 3PM to 4PM, Monday through Thursday. - Ensure the DNS server properly links scottastrong.org to the instructor's website. - Students to check the course web space and familiarize themselves with the syllabus and course materials. - Students to interact with the Hi TA system for pre-lecture and post-lecture activities. - Students to complete 75% of the generative AI interactions to pass the course. - Students to complete six homework assignments with five questions each. - Students to engage in micro projects for higher grades. ## Key Decisions - The course will use specifications grading, requiring students to complete a certain percentage of tasks to pass. - Generative AI will be integrated into the course to assist with coding and learning. - Students can choose to use MATLAB, Python, or R for their coding assignments. - Office hours will be held in Stratton Hall 102 and the classroom after lectures. ## Notes and Observations - The course, MATH307A, is an introduction to scientific computing, designed for applied scientists and engineers. - The instructor, Scott Strong, has provided a detailed overview of the course structure, including meeting times, office hours, and grading criteria. - The course will meet Monday through Thursday from 01:15 to 3PM, consisting of two fifty-minute lectures with a five-minute break. - Office hours will be held in Stratton Hall 102 and by appointment, with additional hours after class in the classroom. - The course will utilize a generative AI system, Hi TA, to assist with learning and coding tasks. Students are encouraged to interact with this system for pre-lecture and post-lecture activities. - The instructor has emphasized the importance of engaging with the course material and using the generative AI system to enhance learning. - The course will include six homework assignments, each with five questions, and students are expected to complete 80% of the total problems. - Micro projects will be available for students seeking higher grades, with the opportunity to design their own projects. - The instructor shared personal anecdotes and background information to introduce himself to the class. - Students participated in interactive activities using the Mentimeter system to share their feelings and backgrounds. - The instructor discussed the integration of generative AI in the course and its role in assisting with coding and learning tasks. # 6-24-25 ## MATH307 Scientific Computing - Day 2 Action Items Summary ## Action Items ### For Instructor - Research and implement proper MATLAB program termination commands (alternative to `exit` which closes entire program) - Publish mesh visualization code and AI-generated animation scripts to course website - Create Python equivalent of matrix multiplication implementation for students preferring Python - Add error handling/dimension checking code to matrix multiplication algorithm - Upload Day 2 lecture board photos to website - Update website to split lecture materials into three sections: boards, audio summaries, and notes - Develop additional micro-projects from brainstormed list (prioritize bolded items in queue) - Finalize deliverable format for micro-projects that demonstrates human involvement - Link Canvas gradebook with Hi TA system for seamless grade integration ### For Students - Complete Hi TA lecture reflection for Day 2 (LO2 interactions due before next class) - Export Day 2 Hi TA conversations as markdown files and submit to Canvas - Practice matrix multiplication implementation in chosen programming language (MATLAB/Python/R) - Begin working on Homework Problem 2 using Day 2 concepts - Test and debug individual matrix multiplication code implementations - Familiarize with MATLAB syntax for matrix operations and dimension checking - Review linear transformation concepts and standard basis vector calculations ### Technical Setup - Resolve Python matrix syntax questions for students choosing non-MATLAB environments - Ensure all lab computers have proper MATLAB access for logged-in students - Test Hi TA system export functionality and troubleshoot three-dots menu access ## Key Decisions ### Programming Implementation - Matrix multiplication will be implemented from scratch using triple nested loops before using built-in functions - Error handling for incompatible matrix dimensions will be added to student implementations - MATLAB chosen as primary demonstration language, with Python support available - Students encouraged to understand computational cost (O(N³)) before using optimized library functions ### Visualization Approach - AI-generated animated visualizations will supplement static grid transformations - Mesh plotting codes will be provided to make abstract linear transformations tangible - Students will visualize how 2x2 matrices transform the coordinate plane through standard basis vectors ### Assessment Integration - Hi TA interactions remain separate from Canvas initially (integration planned for future) - Markdown export from Hi TA conversations required for Canvas submission - Checkbox function in Hi TA activities unclear - students should verify completion through bot interaction ### Course Content Progression - Matrix multiplication mastery required before advancing to eigenvalue/eigenvector topics - Theoretical understanding must be paired with computational implementation - Linear transformation properties (linearity, origin preservation, parallel line preservation) established as foundation ## Notes and Observations ### Technical Challenges Encountered - Live coding session demonstrated real debugging process when `exit` command terminated entire MATLAB program - Student confusion about Hi TA system navigation resolved (conversation view vs activity view for export) - Matrix dimension compatibility errors successfully demonstrated to show importance of error checking - Semicolon behavior in MATLAB clarified (suppresses output display but doesn't prevent execution) ### Student Engagement Patterns - Strong interest in animated visualizations over static grid plots - Questions about programming language choice (MATLAB vs Python) indicate thoughtful consideration - Students successfully following along with live matrix multiplication implementation - Active participation in geometric interpretation of linear transformations ### Pedagogical Insights - Animated transformations significantly improved conceptual understanding compared to before/after static images - Connection between determinant sign and geometric orientation (flip vs no flip) effectively demonstrated - Standard basis vector approach successfully simplified understanding of plane transformations - Real-world analogies (rotation, mirror reflection) helped contextualize abstract linear algebra ### Course Infrastructure - Hi TA system functioning well for learning objectives but Canvas integration needed - Website organization proving effective with embedded homework and project descriptions - Course material progression from symbolic math to computational implementation working smoothly - Balance between theoretical understanding and practical coding skills being maintained ### Future Session Preparation - Eigenvalue/eigenvector introduction planned for Day 3 - More complex transformation examples needed to build toward eigenspace concepts - Error handling implementation priority for next coding session - Additional micro-project details to be published based on student interest areas # 6-25-25 ## Action Items - Review lecture pictures and learning reflections. - Prepare for discussions on matrix transformations and eigen problems. - Get matrix multiplication code up and running with error handling. - Start working on the matrix multiplication runtime project. - Look into error handling in MATLAB and Python. - Prepare for discussions on regular stochastic matrices. ## Key Decisions - Learning objectives for Taylor series will be postponed until the matrix topics are completed. - A new project on matrix multiplication runtime has been introduced. ## Notes and Observations - The lecture focused on matrix transformations, eigen problems, and their applications. - Learning objectives (LOs) for Taylor series are not yet available as the class is still covering matrix topics. - Matrix multiplication codes are available in MATLAB and Python, with potential ports to R or Mathematica if needed. - Discussion on computational costs and error handling in MATLAB and Python. - Introduction to a new project on matrix multiplication runtime, comparing custom code against built-in algorithms. - Detailed explanation of matrix transformations, including shearing and dilation, with examples. - Discussion on eigenvalues and eigenvectors, including their calculation and significance in matrix transformations. - Introduction to regular stochastic matrices and their properties, including the concept of a stationary vector. - Example of a Markov chain with a radio station playing two genres, illustrating the concept of a stationary distribution. - Use of MATLAB to calculate eigenvalues and eigenvectors, demonstrating the application of linear algebra concepts. ## Additional Topics - The lecture included a humorous interlude with a joke to lighten the mood. - The session concluded with a discussion on the application of matrices in real-world scenarios, such as demographics and radio station transitions. # 6-26-25 ## Action Items - Review the two posted projects on matrix multiplication and image compression. - Prepare a five to seven-minute video explaining the project work and code. - Consider the feasibility of creating the video and discuss any media constraints. - Start working on the matrix multiplication project as it is relevant to class discussions. - Check the codes posted on HiTA and review the transformation of the grid code. - Organize and linearize handwritten and code submissions for homework. - Prepare for a discussion on Taylor series and related problems on Monday. - Submit homework by next Wednesday, with a new assignment to be released on Tuesday. ## Key Decisions - The projects will involve a mixture of mathematics and coding, with a reflection and video component. - Homework submissions will accept multiple formats, including handwritten and code files. - The due date for the current homework has been extended to next Wednesday. ## Notes and Observations - Two projects have been posted: one on matrix multiplication and another on image compression using eigen information. These projects aim to build a larger code base with generative AI systems. - Deliverables include a one-page reflection and a video walkthrough of the project and code. - The instructor emphasized the importance of understanding the code and not relying solely on AI-generated solutions. - Discussion on the use of blue books for exams and the shift towards ensuring human involvement in work. - Codes related to class topics are available on HiTA, including a transformation of the grid code. - The instructor demonstrated the process of creating Taylor polynomials and estimating errors using MATLAB. - The class explored the use of Taylor series for approximating functions and discussed the importance of understanding the error bounds in approximations. - The instructor provided guidance on using MATLAB for plotting and analyzing functions, emphasizing the importance of understanding vector operations in MATLAB. - The session included a detailed walkthrough of creating and analyzing Taylor polynomials, with a focus on understanding the geometric information captured by derivatives. - The instructor addressed questions about the projects, homework, and the use of Taylor series in scientific computing. # 6-30-25 ## Overview Today’s class focused on: 1. **Administrative adjustments** to homework and project allocations. 2. **Taylor series fundamentals**: definition, polynomial approximations, and remainder. 3. **MATLAB coding practice** to implement Taylor series approximations for $e^x$ and $\sin(x)$. 4. **Numerical differentiation** derived from Taylor expansion, introducing first-order finite difference approximations and setting up context for future higher-order methods. ## Instructor Highlights - Workflow streamlining for AI grading and assignment posting. - Upcoming projects to integrate multivariable calculus, linear algebra, and visualization. - Strong emphasis on **coding generality** and building functions modularly. ## Next Steps - Homework 1 due Wednesday 11:59 PM (Problem 5 moved to project). - Homework 2 to be released tomorrow. - Continue development of numerical differentiation techniques using Taylor series expansions next class. # 7-1-25 ## Action Items - Upload location on Canvas to be opened next Monday for project deliverables. - Homework 1 is due tomorrow; remember there is no problem 5. - Homework 2 will be posted tomorrow. - Prepare for the last class on Thursday, 07/11. ## Key Decisions - Two more projects have been posted. - Problem 5 from Homework 1 has been moved to a project due to its length. - The course has shifted focus to calculus earlier than usual to align with summer energy levels. ## Notes and Observations - The lecture focused on finite difference approximations, truncation versus round-off error, and Taylor series. - The instructor plans to provide feedback through audio transcriptions to expedite the process. - The class is currently discussing finite difference approximations to derivatives and truncation versus round-off error. - The instructor explained the importance of Taylor series in scientific computing, particularly in constructing derivatives computationally. - A detailed explanation of how to derive finite difference formulas for first, second, and third derivatives was provided. - The instructor demonstrated the use of MATLAB to construct Taylor series approximations and discussed the limitations of finite precision arithmetic. - The lecture included a discussion on the implications of using small step sizes (h) in numerical differentiation and the potential for round-off errors. - The instructor emphasized the importance of understanding the trade-off between truncation error and round-off error in computational mathematics. - The class was encouraged to think about the implications of finite precision arithmetic and how it affects numerical computations. - The instructor shared insights on the historical context of Taylor series and their application in solving complex equations before the advent of modern computational power. ## Additional Information - The instructor plans to sync lecture objectives with Canvas, though they are currently behind. - The class is encouraged to use High TA for lecture reflections and activities. - The instructor mentioned the possibility of testing new features on the High TA platform. # 7-2-25 ## Action Items - Complete Homework #1 by tonight. - Review Homework #2, which is now posted on the website, due next Wednesday. - Finalize and post additional projects as soon as possible. - Check and update lecture objectives and due dates for upcoming classes. ## Key Decisions - Homework #1 is due tonight, and Homework #2 is due next Wednesday. - Lecture objectives and activities will be streamlined and updated regularly. ## Notes and Observations - The lecture focused on numerical methods, particularly finite difference approximations and their implications in computational environments. - Discussion on grading scale: A starts at 93% in the plus-minus grading system. - Explanation of how projects are structured with two-part values for completion. - Detailed explanation of finite difference methods, including first, second, and third derivatives, and their implementation in MATLAB. - Emphasis on the importance of understanding machine number lines and the implications of finite precision arithmetic. - Discussion on round-off errors and their impact on numerical calculations. - Explanation of floating-point arithmetic, including the significance and exponent in machine numbers. - Demonstration of MATLAB coding practices for separating functions into files for better code management. - Discussion on the challenges of numerical integration and the importance of understanding truncation and round-off errors. - Explanation of the limitations of machine number lines and the non-uniform gaps between machine numbers. - Discussion on the implications of these gaps for numerical calculations, including examples with MATLAB and theoretical explanations. - Emphasis on the importance of understanding the trade-offs between precision and scale in computational environments. - Explanation of the conditions under which round-off errors become significant and how to estimate the point at which they overtake truncation errors. - Encouragement to be aware of potential errors when performing numerical calculations, especially when dealing with small numbers or large scales.