Think about preparing a thesis statement that responds to ONE of the following essay questions, using appropriate course content as your evidence.

If you are preparing for this aspect of the final exam now, I would suggest first carefully read the essay questions. Determine – what is the question asking you? Then, go for a walk. Think about it, and determine your own point of view. Next, look back at our course materials. What evidence can you use to argue for your point of view? The evidence you use needs to demonstrate your knowledge of course content – your examples must come from the course content. And last but not least – you need to define your terms, so you know what you mean when you use those words. A good argument and tight logic requires a precise understanding of concepts.  

In your essay, you may refer to any course readings, lectures, or activities you feel would help you make the best historical argume nt to support your thesis claim. When you refer to course content in your essay, best practice would be to put in round brackets ( ) at the end of a sentence, the name of the author, or title of the lecture, or number of the activity, from which you draw that particular point, argument, idea or fact. This is a casual way of citing your sources, more casual than what I asked for in the historical essay assignment, but still requiring you to practice giving credit where appropriate.

In terms of the length of your essay. I am asking for a four-paragraph answer. An introduction and three body paragraphs. Each paragraph should contain a sub argument. The paragraph should identify what episode from history you have chosen to support your thesis statement, and then in the paragraph you need to make connections between that past event and the claim you have made. That means in each paragraph you are going to tell me some details about that past event but also why those details are relevant in terms of providing evidence to support your thesis claim.

Choose one of the following questions and answer it in the form of an essay. Your essay should have a clear and identifiable thesis statement and should be organized into several paragraphs. Three different episodes from the history of mathematics as drawn from our course materials should be used as historical evidence with which you support your thesis claim. At the end of your essay, a one to two sentence conclusion will be sufficient.

Q1. Mathematics and Society

Is mathematics separate from society? Have cultural beliefs and social values limited the ways in which mathematicians have practiced or invented mathematics? Or have mathematical developments had significant impact on society in modern history? Develop a thesis statement about the relationship between mathematics and society and draw upon three different examples from the course as evidence to support your claim.

Q2. Philosophy and the Limits of Mathematics

Does our philosophical belief system change what we might consider to be legitimate entities in mathematics? At times mathematical expressions once deemed inadmissible in mathematics have become foundational ideas for whole branches of the subject. Pick a philosophy of mathematics introduced in this course, defining your chosen position in the introduction to your essay. Taking as your examples complex numbers, Cantoràtransfinite set theory and non-Euclidean geometry, argue whether or not your philosophy admits or denies these mathematical entities and theories. Justify your claims using the criteria of the philosophical position you have chosen.