Update README.md

README.md

@@ -162,8 +162,6 @@ It performs best when explaining every intermediate step before arriving at the
 |-----------|----------|
 | Arithmetic | Addition, Subtraction, Multiplication, Division |
 | Algebra | Linear Equations, Quadratic Equations, Polynomial Factorization |
-| Geometry | Angles, Triangles, Circles, Coordinate Geometry |
-| Calculus | Differentiation, Integration, Limits |
 | Statistics | Mean, Median, Mode, Variance, Standard Deviation,etc.|
 
 ##  Fundamental Mathematical Formulae
@@ -172,8 +170,6 @@ It performs best when explaining every intermediate step before arriving at the
 |---------|----------|
 | Quadratic Formula | $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ |
 | Pythagorean Theorem | $a^2+b^2=c^2$ |
-| Distance Formula | $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ |
-| Midpoint Formula | $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ |
 | Slope Formula | $m=\frac{y_2-y_1}{x_2-x_1}$,etc. |
 
 ---
@@ -270,4 +266,175 @@ outputs = model.generate(
 )
 print(tokenizer.decode(outputs[0], skip_special_tokens=True))
 ```
+---
+
+# 📊 Applications
+
+This model is designed for a wide variety of mathematical and scientific applications.
+
+- 📚 AI Tutors
+- 🎓 STEM Education
+- 🤖 Mathematics Chatbots
+- 🔬 Scientific Computing
+- 📝 Homework Assistance
+- 🧪 Research
+- 💻 Educational Software and more.
+
+---
+# Limitations
+
+Although highly capable, the model has several limitations.
+
+- May occasionally make arithmetic mistakes on extremely long calculations.
+- Complex symbolic manipulations should always be verified.
+- Does not replace professional Computer Algebra Systems (CAS) such as Mathematica or Maple.
+- Performance depends heavily on prompt quality.
+- Mathematical proofs may require human verification.
+- May hallucinate unsupported mathematical identities if prompted incorrectly.
+- Numerical approximations can accumulate rounding errors.
+- High-stakes scientific applications should always be independently validated.
+- Performance may decrease on very large expressions or lengthy derivations.
+
+---
+#  Future Improvements
+
+Future releases may include:
+
+- Better symbolic reasoning
+- Olympiad-level mathematics
+- Interactive tutoring
+- Diagram understanding
+- Mathematical OCR support
+- Scientific equation solving and more.
+---
+
+#  Acknowledgements
+
+Special thanks to:
+
+- Adaption Labs
+- Mixtral Team
+- Hugging Face and Kaggle 
+- Transformers Community
+- Open-source AI Community
+- Mathematical research contributors
+ 
+---
+
+#  Citation
+
+If you use this model in your research, please cite:
+
+```bibtex
+@misc{adaptive_math_reasoner,
+  title        = {Adaptive Math Reasoner},
+  author       = {Edidiong Charlie},
+  year         = {2026},
+  publisher    = {Hugging Face},
+  model        = {Mixtral-8x7B-Instruct},
+  framework    = {Adaption Labs + AutoScientist},
+  license      = {Apache-2.0},
+  url          = {https://huggingface.co/Charlie890/Adaptive-Math-Reasoner-Mixtral-8x7B}
+}
+```
+---
+
+#  License
+
+This project is released under the **Apache License 2.0**.
+
+You are free to:
+
+- ✅ Use commercially
+- ✅ Modify
+- ✅ Distribute
+- ✅ Private use
+- ✅ Research
+- ✅ Education
+
+Subject to the terms and conditions of the Apache License 2.0.
+
+---
+# Performance Goals
+
+The model is optimized to:
+
+- Produce step-by-step mathematical reasoning.
+- Solve algebraic equations accurately.
+- Handle advanced calculus problems.
+- Solve geometry and trigonometry questions.
+- Perform statistical computations.
+- Explain mathematical concepts clearly.
+- Generate clean LaTeX mathematical expressions.
+- Assist students, educators, engineers, and researchers.
+
+---
+
+#  Example Prompt Ideas
+
+```text
+Solve:
+3x² + 7x - 10 = 0
+```
+```text
+Differentiate:
+
+f(x)=sin(x)e^x
+```
+```text
+Integrate:
+
+∫x²cos(x)dx
+```
+```text
+Find the determinant of
+
+|2 4|
+|1 5|
+```
+```text
+Prove the Binomial Theorem.
+```
+```text
+Explain Bayes' Theorem with a practical example.
+```
+```text
+Find the eigenvalues of the matrix:
+
+[[4,2],
+ [1,3]]
+```
+
+---
+
+# Mission
+
+The goal of **Adaptive Math Reasoner** is to provide accurate, explainable, and accessible mathematical reasoning powered by modern Large Language Models.
+
+The project aims to make advanced mathematics easier to learn, explore, and apply across education, engineering, science, finance, and research.
+
+---
+
+## Version
+
+**Version:** 1.0.0
+
+**Base Model:** Mixtral-8x7B-Instruct
+
+**Framework:** Transformers
+
+**License:** Apache-2.0
+
+**Primary Domain:** Mathematical Reasoning
+
+**Author:** Edidiong Charlie
+
+---
+
+# Thank You
+
+Thank you for using **Adaptive Math Reasoner**.
+
+We hope this model helps students, educators, researchers, developers, engineers, and the open-source community solve mathematical problems more effectively.
 
+Happy building with AI and Mathematics! 🚀