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Exploring Foundations in Mathematics
Exploring Foundations in Mathematics
This section presents a selection of readings that delve into the deeper ideas and historical development of mathematics. Each article is designed to enrich your understanding by revealing the concepts, reasoning, and evolution behind the math we study today. These are not traditional exercises, but intellectual explorations which are meant to inspire curiosity and foster a more profound appreciation for the structure and beauty of mathematics.
Evolution of the Function Concept: A brief Survey
Evolution of the Function Concept: A brief Survey
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Kleiner, I. (1989). Evolution of the Function Concept: A Brief Survey. The College Mathematics Journal, 20(4), 282–300. https://doi.org/10.1080/07468342.1989.11973245
Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.
Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.
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Grabiner, Judith V. “Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus.” The American Mathematical Monthly, vol. 90, no. 3, 1983, pp. 185–94. JSTOR, https://doi.org/10.2307/2975545. Accessed 16 July 2025.
The Function sin x / x
The Function sin x / x
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Gearhart, W. B., & Shultz, H. S. (1990). The Function . The College Mathematics Journal, 21(2), 90–99. https://doi.org/10.1080/07468342.1990.11973290
Leibniz and the Spell of the Continuous
Leibniz and the Spell of the Continuous
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Grant, H. (1994). Leibniz and the Spell of the Continuous. The College Mathematics Journal, 25(4), 291–294. https://doi.org/10.1080/07468342.1994.11973624
Historical Perspectives on Mathematical Thought
Historical Perspectives on Mathematical Thought
This collection highlights the evolution of key mathematical concepts through a historical lens. From ancient reasoning to modern interpretations, these articles explore how foundational ideas emerged, developed, and continue to influence the way we teach and learn mathematics today.
Mathematical Firsts—Who Done It?
Mathematical Firsts—Who Done It?
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WILLIAMS, RICHARD H., and ROY D. MAZZAGATTI. “Mathematical Firsts—Who Done It?” The Mathematics Teacher, vol. 79, no. 5, 1986, pp. 387–91. JSTOR, http://www.jstor.org/stable/27964949. Accessed 16 July 2025.
The Spider's Spacewalk Derivation of sin' and cos'
The Spider's Spacewalk Derivation of sin' and cos'
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Hesterberg, Tim. “The Spider's Spacewalk Derivation of sin' and cos'.” College Mathematics Journal 26 (1995): 144-145.
Sines & Cosines of the Times
Sines & Cosines of the Times
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Katz, V. J. (1995). Sines & Cosines of the Times. Math Horizons, 2(4), 5. https://doi.org/10.1080/10724117.1995.11974925
The Lengthening Shadow: The Story of Related Rates
The Lengthening Shadow: The Story of Related Rates
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Austin, Bill, et al. “The Lengthening Shadow: The Story of Related Rates.” Mathematics Magazine, vol. 73, no. 1, 2000, pp. 3–12. JSTOR, https://doi.org/10.2307/2691482. Accessed 16 July 2025.
The Falling Ladder Paradox.
The Falling Ladder Paradox.
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Scholten, Paul, and Andrew Simoson. “The Falling Ladder Paradox.” The College Mathematics Journal, vol. 27, no. 1, 1996, pp. 49–54. JSTOR, https://doi.org/10.2307/2687275. Accessed 16 July 2025.
Mathematical Modeling and the Evolution of Motion
Mathematical Modeling and the Evolution of Motion
This collection explores how mathematical thinking has historically shaped our understanding of motion and mechanics. Through applications ranging from aircraft descent patterns to rotating sprinklers, these articles highlight the role of calculus and modeling in interpreting and solving real-world problems.
Design of an Oscillating Sprinkler
Design of an Oscillating Sprinkler
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Braden, B. (1985). Design of an Oscillating Sprinkler. Mathematics Magazine, 58(1), 29–38. https://doi.org/10.1080/0025570X.1985.11977144
How Not to Land at Lake Tahoe!
How Not to Land at Lake Tahoe!
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Barshinger, R. (1992). How Not to Land at Lake Tahoe! The American Mathematical Monthly, 99(5), 453–455. https://doi.org/10.1080/00029890.1992.11995874
Why Women Succeed in Mathematics
Why Women Succeed in Mathematics
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Fabricant, Mona, Sylvia Svitak, and Patricia Clark Kenschaft. "Why Women Succeed in Mathematics". The Mathematics Teacher 83.2 (1990): 150-154. < https://doi.org/10.5951/MT.83.2.0150>. Web. 16 Jul. 2025.
Graphs of Rational Functions for Computer Assisted Calculus
Graphs of Rational Functions for Computer Assisted Calculus
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Byrd, Stan, and Terry Walters. “Graphs of Rational Functions for Computer Assisted Calculus.” The College Mathematics Journal, vol. 22, no. 4, 1991, pp. 332–34. JSTOR, https://doi.org/10.2307/2686239. Accessed 16 July 2025.
Foundations and Evolutions of Mathematical Ideas
Foundations and Evolutions of Mathematical Ideas
This section highlights elegant, visual, and historical perspectives on fundamental mathematical concepts. From visual proofs that illustrate the beauty of geometry to an in-depth historical narrative on how integration evolved from antiquity to modern analysis, these articles offer a deeper appreciation of both the intuition and rigor behind the mathematics we study today.
Looking at ∑k=1nk and ∑k=1nk2 Geometrically
Looking at ∑k=1nk and ∑k=1nk2 Geometrically
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Hegblom, Eric. "Looking at ∑k=1nk and ∑k=1nk2 Geometrically". The Mathematics Teacher 86.7 (1993): 584-587. < https://doi.org/10.5951/MT.86.7.0584>. Web. 16 Jul. 2025.
Proof without words: Area of a Disk is πR2
Proof without words: Area of a Disk is πR2
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Hendel, R. J. (1990). Proof without words: Area of a Disk is πR2. Mathematics Magazine, 63(3), 188. https://doi.org/10.1080/0025570X.1990.11977516
The Evolution of Integration
The Evolution of Integration
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Shenitzer, A., and J. Steprāns. “The Evolution of Integration.” The American Mathematical Monthly, vol. 101, no. 1, 1994, pp. 66–72. JSTOR, https://doi.org/10.2307/2325128. Accessed 16 July 2025.
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