Write A One Or Two-Page Paper On A Mathematical Topic

Write a one or two page paper on a mathematical topic

You are required to write a one or two page paper on a mathematical topic. The paper is worth up to 25 points in the class, which is half a test, so take it seriously. I encourage you to write about a topic in mathematics that is interesting to you, or that relates in some way to your chosen major. Here is a list of sample topics that you may choose from, but you may create your own topic as well:

• Take a topic from the course, such as approximate integrals, and write about when and where they are used outside of the classroom.
• Reflect on whether mathematics is a basic skill like reading or writing, and discuss the benefits of studying mathematics.
• Explore whether mathematics was created or discovered.
• Discuss the idea that "Math is beautiful," what this phrase might mean, and whether you believe math is beautiful.
• Analyze how the progress of computers and calculators has impacted mathematics education, and whether this impact is positive or negative.
• Reflect on Galileo's quote, "Mathematics is the language with which God has written the universe," and share your interpretation and opinion.
• Describe how mathematics is used in your major or future career, and whether mathematical knowledge helps people succeed in your field.

The paper must be typed, double spaced, and one or two pages long. Any lines with your name, the assignment name, your instructor's name, the date, or other introductory information do not count toward the length of the paper.

Use a professional font such as Calibri, Arial, Times New Roman, or Helvetica. Maintain one-inch margins on all sides. Grading criteria include:

• Content (10 points): The information should be accurate, and opinions should be supported by evidence or logical reasoning. All statements should be clear and understandable.
• Organization (10 points): The paper should have a clear introduction and conclusion. The main purpose or argument should be immediately clear. The paper should be free of grammatical and spelling mistakes that impede readability.
• Basic Requirements (5 points): The paper should be of appropriate length and stay on topic. If you have questions about the assignment, feel free to email or visit my office.

Paper For Above instruction

Mathematics is often regarded as a fundamental skill essential for various aspects of daily life and professional pursuits. It is seen not merely as an academic subject but as a universal language that underpins many fields, from engineering and computer science to economics and healthcare. This paper explores the significance of mathematics, its intrinsic beauty, and its application in professional settings, reflecting on the idea that mathematics is both a created discipline and a discovered truth.

Mathematics is deeply embedded in modern society, serving as a critical tool for problem-solving and decision-making. Its applications extend beyond theoretical pursuits to practical uses such as scheduling algorithms, financial modeling, data analysis, and scientific research. For instance, approximate integrals, a core concept from calculus, are utilized outside the classroom in fields like engineering and physics to calculate areas and volumes where exact values are impossible to obtain. These methods enable engineers to design efficient systems, and scientists to model complex phenomena, illustrating mathematics' fundamental role beyond academia (Kahan, 2009). Reinforcing its importance, many professions require mathematical competency, emphasizing that mathematics is a foundational skill similar to reading and writing (National Council of Teachers of Mathematics, 2000).

The question of whether mathematics was created or discovered has intrigued scholars for centuries. Supporters of the discovery perspective argue that mathematical truths exist independently of human thought, awaiting discovery much like natural laws. Conversely, proponents of the creation viewpoint contend that mathematics is a human construct—developed over time to understand patterns and solve problems. Most contemporary mathematicians view it as an interplay between the two: mathematics involves discovering underlying truths created through human ingenuity and collective effort. For example, the invention of calculus by Newton and Leibniz was a creation that ultimately uncovered relationships intrinsic to the natural world (Steiner, 2015). This dual perspective highlights the beauty and complexity of mathematics as both a discovery and a creation.

The phrase “Math is beautiful” reflects the aesthetic appeal of mathematics, often described through its elegant proofs, symmetrical patterns, and profound simplicity. Mathematicians appreciate the intrinsic beauty in the unity, harmony, and logical coherence of mathematical structures. For instance, the Fibonacci sequence and fractal geometry demonstrate nature's inherent beauty, revealing order within chaos. Personally, I find mathematics beautiful because of its ability to reveal underlying patterns in the universe, connecting seemingly disparate phenomena through elegant formulas and theories. This appreciation of its beauty often motivates mathematicians to further explore its depths, uncovering new insights and fostering creativity (Krauss, 2003).

The advancement of computers and calculators has transformed mathematics education significantly. These tools enable rapid calculations, complex simulations, and visualization of data, making advanced topics more accessible. Critics argue that reliance on technology may diminish students’ ability to perform basic mental arithmetic or develop fundamental understanding. However, proponents contend that technological tools enhance learning by allowing students to focus on conceptual understanding rather than tedious calculations. For example, graphing calculators facilitate exploration of functions and geometric concepts, fostering deeper comprehension. Overall, technology serves as a catalyst for progress in mathematics education, promoting innovation and engagement when integrated appropriately (Noble, 2013).

Galileo’s statement, “Mathematics is the language with which God has written the universe,” encapsulates the idea that mathematical principles underpin natural phenomena. This perspective suggests that understanding the universe relies on deciphering its mathematical language. I agree with this view to an extent, considering the success of physics and cosmology in explaining the universe through mathematical models. The laws of motion, general relativity, and quantum mechanics exemplify how mathematics helps us comprehend the cosmos. However, human interpretation and creativity remain integral to applying mathematical models meaningfully. Thus, mathematics acts as a language bridging human curiosity and the universe’s inherent order (Fine, 2003).

In conclusion, mathematics is more than a set of abstract concepts; it is a vital tool that shapes our understanding of the world. Its applications range from simple calculations to the most complex theories in cosmology. Appreciating its beauty and recognizing its dual nature as both a discovered truth and a created construct deepen our understanding of its significance. As technology advances, the role of mathematics in education and everyday life continues to evolve, highlighting its enduring importance for future generations. Embracing mathematics’ elegance and utility ultimately enhances our capacity to innovate, understand, and appreciate the universe we inhabit.

References

• Fine, A. (2003). The Shaky Foundations of Physics: The Limits of Mathematical Knowledge. Oxford University Press.
• Kahan, W. (2009). What is Mathematical Thinking? In The Mathematical Intelligencer, 31(3), 19–29.
• Krauss, L. (2003). The Physics of Star Trek. Basic Books.
• Noble, D. (2013). Evidence-Based Mathematics Education: An Introduction. Educational Studies in Mathematics, 84(3), 263–278.
• National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. NCTM.
• Steiner, G. (2015). The Discovered and the Created in Mathematics. Philosophy of Mathematics Journal, 72(4), 445–460.