References

Textbooks

1. Kenneth H. Rosen, "Discrete Mathematics and Its Applications," 8th Edition, McGraw Hill Education, 2018. (Chapter 6: Counting and Binomial Theorem)

2. Ralph P. Grimaldi, "Discrete and Combinatorial Mathematics: An Applied Introduction," 5th Edition, Pearson, 2003. (Chapter 2: The Binomial Theorem and Pascal's Triangle)

3. Richard Johnsonbaugh, "Discrete Mathematics," 8th Edition, Pearson, 2017. (Section 5.3: Pascal's Triangle and the Binomial Theorem)

Online Resources

Educational Websites

1. Khan Academy: "Pascal's Triangle and Binomial Expansion"

   • Introduction to Pascal's Triangle
   • Patterns in Pascal's Triangle

2. Brilliant.org: "Pascal's Triangle"

   • Properties and Applications
   • Interactive Explorations

3. GeeksforGeeks:

   • Pascal's Triangle Implementation
   • Applications of Pascal's Triangle

4. Wolfram MathWorld: "Pascal's Triangle"

   • Detailed Mathematical Properties

Video Lectures

1. NPTEL Courses:

   • Discrete Mathematics - Binomial Coefficients and Pascal's Triangle
   • Combinatorics and Applications

2. MIT OpenCourseWare:

   • Mathematics for Computer Science - Binomial Theorem

Research Papers and Articles

1. Weisstein, Eric W. "Pascal's Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PascalsTriangle.html

2. Conway, J. H., & Guy, R. K. (1996). "The Book of Numbers." Springer-Verlag. (Chapter on Pascal's Triangle and its Properties)

Interactive Tools and Visualizations

1. GeoGebra: "Interactive Pascal's Triangle"

   • Dynamic Visualization

2. NCTM Illuminations: "Pascal's Triangle"

   • Interactive Learning Tool

Additional Resources

1. The On-Line Encyclopedia of Integer Sequences (OEIS):

   • Pascal's Triangle Sequences
   • Related Number Patterns

2. Mathematical Association of America:

   • Explorations in Pascal's Triangle