HONORS CONTRACT: MATH 16500 (FALL 2023)
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Introduction: During the fall semester of my junior year of college, I conducted an honors contract working closely with Professor Doan Le in the Math Department at IUI. I sought to create a Python program capable of calculating derivatives using computational methods we were being taught in class. This artifact demonstrates the flexible nature of honors contracts to current and future honors students. This is important to acknowledge because honors contracts offer honors students a way to earn honors credits while developing necessary skills in the domain in which they see themselves long term, in my case, it is computer science and research.
Applying Computer Science to Solve Problems in Calculus
Program Created by: Austin Kitch
Contract
Contract
Applying Computer Science to Solve Problems in Calculus
For my Honors contract in MATH16500: Applying Computer Science to Solve Problems in Calculus, I will explore ways that concepts in Calculus problems can be solved using Computer Science and programing. I will figure out how I can create a program to solve problems in Calculus which is a field that works hand in hand with the software sector. I will create a program that can be utilized to solve derivatives using user input. As the semester goes on and more concepts are taught, I will upgrade my program to incorporate other concepts thus improving the program’s functionality and broadening its abilities to solve complex calculus problems. I will share this program with my Professor and demonstrate how it can be helpful in her field of expertise. Along with creating a program to solve these problems successfully, I will be sure to keep organized documentation of the steps, thought processes, obstacles, and solutions found along the way. This project will contribute to my skillset as a problem solver, common misconceptions regarding math not being applicable in real world settings, and knowledgeable application practices for future IUPUI students to potentially reflect on. Upon completion of these problems, I will write a reflection paper between 500-800 words that will wrap up my experiences and take aways from this course and project.
September 6th: Formalize Honors Contract
September 20th: Complete Algorithm
September 25: Complete Pseudocode
October 9th: Meet with Professor to Discuss if Formulas and Logic is Sound
October 25th: Complete Program Capable of Solving Derivatives
November 1st: Discuss Additional Concepts to Add to Program with Professor
November 15th: Have Additional Features Complete
November 20th: Final Touches and Project Presentation
Calculus Concepts Covered
Calculus Concepts Covered
Reimann Sum
Graphing/Visuals
Derivative Calculations
Power Rule
Constant Rule
Product Rule
Quotient Rule
Chain Rule
Visuals of Some Code
Function to Compute Riemann Sum (Left Method)
Function to Compute Riemann Sum (Left Method)
Function to Compute Riemann Sum (Right Method)
Function to Compute Riemann Sum (Right Method)
Reflection: This honors experience helped me grow as a student, prospective scientist, and prospective graduate student. I grew independence and confidence in my ability to solve high-level mathematics utilizing my programming skills. I went into the experience with an open-minded approach to creating this program, and in turn this experience forged a sense of confidence in my abilities to come up with abstract solutions to mathematical problems. I developed this program using the calculus methods I learned from Professor Doan Le while implementing my Computer Science skills. This honors contract helped construct my programming skills and further prepared me for graduate school where I hope to obtain a PhD.
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