Additional Mathematics Pure And Applied Free Download
Genciana Haggins
When I got to Harvard as a first-year student, I had some idea of what I wanted to study. I was a STEM-oriented student, but I was also a music lover and open to learning about new disciplines. Math was a subject I was planning on continuing so I could have a solid foundation in science classes. I then learned that there were two types of math I could study: pure mathematics and applied mathematics. Initially, I felt slightly overwhelmed because I had never heard of the distinction before; I thought math was just math! Luckily, both the Math and Applied Mathematics departments have very helpful and kind people who are here to help students.
Logistically, pure mathematics requires 12 courses (48 credits), of which 8 are in the math department and four are in math or related subjects. Applied mathematics requires 14-15 courses, including five courses in a chosen application area. Happily, if you are not sure which to choose, but you do know you want to study mathematics, many courses overlap and will count for both concentration requirements.
In terms of what differs between the two concentrations, it is actually pretty intuitive! Essentially, pure mathematics focuses on abstract and theoretical concepts in math working to prove theorems and research and discover new realms of math. Pure math courses are heavily proof-based and deal with theoretical possibilities of math. On the other hand, applied mathematics focuses on ways to use math. This is why all students choose a specific application area within their applied math concentration. For example, many students choose economics as their application area and take courses learning the mechanics of how to use math in economic situations.
Math is also interdisciplinary. Last semester, I took Applied Math 50: Introduction to Applied Mathematics. In this class, we learned about many different areas of study in math, including topics like epidemiology, game theory and network theory. The exposure to many different subjects helped us all gain an understanding of what sorts of processes and systems math can help create and also see how they might relate. Many processes that help create models in one subject, like epidemiology, can also be used in the same way to learn how connected humans are socially. The end of the class concluded with a final project where we used coding skills and math processes we had learned about to research our own topic. My group decided to study how the attributes of popular music in the U.S. affect their chart rating. It was fascinating to combine music and math together and come out with analyses from the data.
Both concentrations are highly useful for gaining a broad and comprehensive understanding of math that will help students in the workforce or in further academic endeavors. Math is simply everywhere and serves as the backbone to many systems we rely on every day and might even take for granted.
Before I start my question, I should probably mention that this question might not be the right question to ask here, but I tried academiabeta, and stackoverflow, but without getting any to-the-point responses. I also noticed that there were some questions of similar interest asked here, but mine is little different and more subject/situation-specific. Also I am afraid my question might be a little too long, pardon my slightly unnecessary detail!
Here is my situation: I am a pure mathematician finishing Ph.D., working in Riemann surfaces, Teichmueller theory and differential geometry (with published papers in decent journals), having backgrounds in these topics and some PDE and topology and have some introductory knowledge about programming. I have been wanting to switch to little more applied areas (described below) because: 1) I believe getting posts and grants are slightly easier in there, 2) my postdoc hunting in pure mathematics have resulted in vein (despite getting shortlisted twice in Europe). I wanted to switch later anyway but reason 2) is forcing me to think of it now.
By applied areas, I meant areas like medical imaging, computer vision or even theoretical biology (there are interesting works of Prof. Robert Penner on moduli spaces and protein folding, for example), where they use Riemann surface and differential geometry a lot, and I want to work in more theoretical problems, but would also like to learn more computational techniques (although secondary).
Since I have not published any single papers in those applied areas, or haven't had any formal training in them, what are my chances of getting a postdoc in these areas, being a pure mathematician all my life so far? If any of you have done so before, or are working in these applied areas, I would very much appreciate if you inform me! By informal communication with some people (who are Ph.D. students) working in these areas, I was informed that my backgrounds are good, but one or two professors I have contacted already mentioned that they want somebody with actual research experience in say imaging, which I do not have. So, I am not sure where I stand compared to other applicants. Your responses and honest opinion (even though not in my favor) will be highly appreciated! Thanks a lot in advance!
There is a newish emerging area, `applied algebraic topology'. It includes Topological Data Analysis (see work by Gunnar Carlsson and others). There is also new work again in Applied Algebraic Topology looking at Configuration spaces and probablity theory. Look for research assistant jobs at Post Doc level on specific topics in applied geometry and topology.
There is also an ESF programme ( ) that gives some idea of what may be available. Some of this would provide a half way house between where you are and where you want to be! Good Luck. (Soon there is s summer school in Slovenia on these areas. Look at the program schedule and you may get some ideas on who to contact to see what they think, whetehr there are any positions coming up, short visits are a good way to start if they have money for such and seem interested. I think there is quite a good chance and all of this area is growing fast so it could be very interesting to get into it at the moment. (The topic of big data is even hitting the newspapers, and that forms part of this.)
The funny thing is, getting this job was kind of an accident. When I applied for the job, the job add just said that they were looking for a pascal programmer. I think they never even hoped to find someone with a math background (let alone image processing).
If I were in your position and no other opportunities come up, I'd be looking to get an entry level programmer job in something like laboratory software. This may not entail math at first but provide an opportunity for you to move into that.
Mathematics is the study of quantity, structure, space, and change. Exploring and understanding the world in which we live is increasingly a matter of mathematical inquiry and discovery. Laptops, smartphones, and video game consoles rely on mathematics, as do the techniques engineers and empirical scientists use to probe nature. Consequently, there is growing need for individuals capable of "speaking the language" of mathematics.
Mathematics provides a broad range of career options; students can find employment in many industries including government, technology, insurance, healthcare, statistics, science, manufacturing, research, finance, and academia.
The Pure and Applied Mathematics Concentration of the Master of Science in Mathematics in the College of Basic and Applied Sciences provides students with a deep and comprehensive foundation in advanced mathematics at the Masters' level. Coursework is tailored to meet the individual needs of students and provides preparation for pursuing additional graduate study and/or pursuing employment in diverse quantitative fields.
MTSU's Master of Science in Mathematics gets students involved in both the understanding and creation of advanced mathematics through quality instruction, opportunities for research, and close faculty-student interaction. A high percentage of program graduates enter Ph.D. programs across the country.
Hays Whitlatch earned his M.S. in Mathematics at MTSU following a recommendation from a co-worker and began work on his doctorate at the University of South Carolina in fall 2014. Whitlatch had moved to the Nashville area for a job following his undergraduate studies at the University of Iowa. "It was a great recommendation," he says. "One thing that I really liked about MTSU is that professors are willing to invest much time into curious students such as myself." One of these curious moments led him to the weekly Discrete Mathematics seminars where he discovered a passion for graph theory. Whitlatch, who wrote his thesis on "Isoperimetric Constants in Planar Graphs with Hyperbolic Properties," ultimately wants to teach and research in a university environment. His graduate teaching assistantship helped him both financially and in his development as an educator.
MTSU alum Fengqing "Zoe" Zhang (M.S. in Mathematics, 2010) joined Drexel University as assistant professor in fall 2014 after finishing her Ph.D. in Statistics at Northwestern University. She completed her MTSU master's thesis on "Imaging Mass Spectrometry Data Analysis with Applications in Cancer Study" under the supervision of Dr. Don Hong. The work led to three journal publications and earned the 2011 Master's Thesis Award for Digital Scholarship from the Conference of Southern Graduate Schools. Reviewers called it "cutting-edge" because linking spectroscopy technology and the applied-statistical method is relatively new work. "During my master's study, I had the chance to attend various seminars and to present my work at regional and national conferences," Zhang says. "My training in mathematics, statistics, and teaching at MTSU provided a foundation for my later study and research." She holds a B.S. in Electrical Engineering from Beijing University of Aeronautics and Astronautics.
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