AI Training for Mathematics
Seth Mariano
About Me
A mathematics trainer working with AI technology, leveraging expertise to enhance AI model performance through prompt engineering, fact-checking, and editing. With a passion for mathematics and a few months of hands-on experience, I strive to push the boundaries of AI-assisted learning.
Table of Contents
Overview of AI Training Tasks
Key Projects & Contributions
Prompt Engineering Highlights
Challenges & Lessons Learned
Future Goals
1. Overview of AI Training Tasks
Fact-Checking AI Responses: Ensuring mathematical accuracy and identifying flaws in AI-generated solutions.
Creating Stump Prompts: Designing challenging problems to test the limits of AI models.
Editing & Enhancing Responses: Improving AI answers to align with educational best practices.
Developing Learning Modules: Helping create adaptive content for students using AI suggestions.
2. Key Projects & Contributions
Project 1: Optimizing AI responses for calculus-based questions.
Project 2: Collaborated on AI enhancements for geometry and algebra modules.
Project 3: Identified and resolved model inconsistencies in probability and statistics responses.
3. Prompt Engineering Highlights
Sample Prompt 1: Stump the AI with non-standard integration questions.
Prompt:
Evaluate the integral ∫ex1+e2x dx\int \frac{e^x}{1 + e^{2x}} \, dx∫1+e2xexdx.
Model Response:
The model provided the solution as:
The approach was correct but lacked intermediate steps, making it difficult for learners to follow.
Improvements Made:
Added step-by-step breakdown:
Substituted u=exu = e^xu=ex, du=ex dxdu = e^x \, dxdu=exdx.
Rewrote the integral in terms of uuu.
Clarified how the solution simplifies to 12arctan(ex)+C\frac{1}{2} \arctan(e^x) + C21arctan(ex)+C.
Included a brief explanation of when to use substitution in similar problems to aid learning.
Sample Prompt 2: Test model limits with multi-variable word problems.
Prompt:
A manufacturer produces two types of products, A and B. Each unit of A requires 2 hours of labor and 3 units of raw material, while each unit of B requires 4 hours of labor and 2 units of raw material. If the manufacturer has 100 hours of labor and 90 units of raw material available, how many units of each product can they produce to maximize profit, given that the profit for A is $30 per unit and for B is $50 per unit?
Model Response:
The model formulated the problem as a linear programming exercise, correctly setting up the objective function:
Subject to the constraints:
However, the model’s solution ended prematurely without exploring all feasible solutions or verifying the corner points.
Refinement:
Completed the solution by calculating the intersection points of constraints to identify the feasible region.
Evaluated profit at each corner point to find the optimal solution.
Provided an alternate solution using the simplex method to demonstrate different solving techniques.
Explained practical applications of linear programming in manufacturing and inventory management.
4. Challenges & Lessons Learned
Adapting to Model Limitations: AI models can sometimes provide partial or overly complex solutions.
Balancing Simplicity and Accuracy: Ensuring answers are mathematically sound yet understandable.
Iterative Improvements: Constant editing is necessary to maintain response quality.
5. Future Goals
Continue developing advanced prompts for deeper model training.
Explore new ways to integrate AI into personalized mathematics learning.
Collaborate with other experts to push the capabilities of AI-assisted education further.
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Posted Oct 17, 2024
Seth developed a customized AI training module specifically for mathematics, which enhanced problem-solving efficiency and accuracy.
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