MATH 15, CLS 15 — Spring 2020 Problem Set 1, Due 24 January 2020
MATH 15, CLS 15 — Spring 2020 Problem set 1, due 24 January 2020 General instructions for the semester: You may use any references you like for these assignments, though you should not need anything beyond the books on the syllabus and the specified web sites. You may work with your classmates provided you all come to your own conclusions and write up your own solutions separately: discussing a problem is a really good idea, but letting somebody else solve it for you misses the point. When a question just asks for a calculation, that’s all you need to write — make sure to show your work! But if there’s a “why” or “how” question, your answer should be in the form of coherent paragraphs, giving evidence for the statements you make and the conclusions you reach. Papers should be typed (double sided is fine) and handed in at the start of class on the due date. 1. What is mathematics? Early in the video you watched, du Sautoy says the fundamental ideas of mathematics are “space and quantity”; later he says that “proof is what gives mathematics its strength.” English Wikipedia tells us “mathematics includes the study of such topics as quantity, structure, space, and change,” while Simple English Wikipedia says “mathematics is the study of numbers, shapes, and patterns.” In French Wikipedia´ we read “mathematics is a collection of abstract knowledge based on logical reasoning applied to such things as numbers, forms, structures, and transformations”; in German, “mathematics is a science that started with the study of geometric figures and calculations with numbers”; and in Spanish, “mathematics is a formal science with, beginning with axioms and continuing with logical reasoning, studies the properties of and relations between abstract objects like numbers, geometric figures, or symbols” (all translations mine).
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