Fitzpatrick Maths

[Rachelle Kun]

DrMatthew Fitzpatrick studied in the Bachelor of Science (Advanced Mathematics) with Honours in mathematics, graduating in 2009, and then did his PhD in mathematics, graduating in 2016. He is now Associate Director of Financial Markets eCommerce at Westpac Institutional Bank.

When I was in high school, I wasn't exactly sure what I wanted to do for a career. I have always had a strong interest in maths and science, and wanted to do something that would be interesting, challenging and also something that would keep my options open. I also had a couple of friends who were doing the same degree, which made the decision slightly easier.

Yes! Since I was very young, anything to do with puzzles, numbers, problem solving or speed calculations was something I really enjoyed. I also had an amazing experience in Year 11 at the National Mathematics Summer School, led by Professor Terry Gagen from the University of Sydney at the time, which cultivated a sincere passion for the subject.

In my honours year, I enjoyed the research component and wanted to see how far I could go with the subject. I was also working part-time in risk at CBA and later at Westpac, and felt that the balance between the bank and postgraduate research worked well. It would help me to build my skills and experience in the subject and help set up a strong career foundation.

I worked in a team that manages automated models that trade spot foreign exchange. In this role, I aimed to make foreign exchange as cheap as possible to trade. That means, we could send out prices with cheaper transaction costs, so customers could trade currencies more efficiently and our bank earned the business. Every day, I conducted research into our prices, the market and our trade decisions, and I also got involved in many different initiatives, that involved our sales teams, customers, regulators and compliance, new products, or various other initiatives, where some multidisciplinary problem solving is required.

Without the degrees, I simply wouldn't qualify to do the work! I use scientific methods and statistical analysis in particular constantly in my job. For example, if we have had a series of profitable and unprofitable trades, we need to separate the signal from the noise and make appropriate decisions that are likely to improve outcomes in the future.

This is advice I received when I was in high school from Professor Terry Gagen at the National Mathematics Summer School: "Always do maths and something." In the professional world, including academia, mathematicians are incredibly valued and useful when they can also do other things, such as play music, communicate with influence, understand a subject where maths is applied, produce art, write stories, or teach others. Your maths knowledge is always enhanced by the "and something".

I can't say much about the difference between Adv Calc and Real Analysis, but if you would be using Royden for your first RA class, it may be pretty challenging. Generally, Royden is used for a first course on measure theory and while it does touch on many of the topic from a first course on analysis, it glosses over a lot of them and omits a lot of stuff.

In many cases Adv. Calc is synonymous with undergrad RA. Based off of a amazon search for Fitzpatrick and Advanced Calc, if you are using: Amazon.com: Advanced Calculus: A Course in Mathematical Analysis: Patrick M. Fitzpatrick: Books

then that appears to be a pretty standard UG RA class; I can't see the table of contents so I don't know for sure, but I would say you are probably much better off taking the Adv Calc course before the Grad Analysis course.

Given your background, you may find it extremely difficult in the grad course since they would assume you are familiar with the 'epsilon-delta' arguments from Fitzpatrick. Also, in Adv Calc, you will learn basic topological concepts on the real line, which you should understand before generalizing to more abstract setting as you would in the grad course. Plus, there will more likely be a higher standard in the grad course since most students have studied analysis at the undergrad level already, while Adv Calc is usually the first course in Analysis,

More importantly, the Adv Calc course will provide the rigor that you need from an analysis course. You will have to think logically and you will get good practice constructing proofs so I think it is sufficient for first year Econ. In first year econ, you may have to think about function spaces or measure theory concepts, but not at a very deep level, and if you do well with Fitzpatrick, you will have the tools to handle these more advanced concepts on your own.

After the first year, you may need to think about more advanced math courses depending on your interests, but you can worry about that when you get there. Also, from a point of view of risk, it is probably better to get in A in Adv Calc than a B or even a C in Analysis.

At Florida State, analysis was considered the easier class (that math majors who had trepidations about taking adv calc would take). At South Florida, you dont have the option to take adv calc and analysis is taught with Rudin. At University of Florida, analysis is considered the tougher class.

My point (if I have one) is that there is considerable variation and flexibility in how these courses are taught (even within a state university system) and you should have opportunity in your application to explain the level and material your course was taught at (even if this amounts to nothing more than listing the text).

If you have the time try first for the advanced calc and then analysis as the first is generally a prerequisite for the latter. It would also help to form a base if you have not taken yet a proof based course in maths.

For your second question i would say both classes are useful for econ but in different levels. So if you want to apply for econ phd eventually both classes would be useful for admissions and for classes.

I remember that the Wired magazine had a Expired/Tired/Wired joke, where they used to write three things, one definitely pass, one representing the current standard, and finally the next thing in the field (usually referred to some technology).

I'm in year 11 and the text books we are using in advanced and extension classes are so horrible. They are made by some dudes named Jones & Couchman. They were published in the 1980s!! Luckily they have been reprinted. We have been having trouble understanding and interpreting some questions (maybe literature/language was different back then), and I'd rather new books that actually explains the various topics of maths in a manner that is easy for us to learn.

I remember using mathscape books from years 7-10 and they were pretty damn good (and they actually had colour too). These stupid Jones and Couchman books have black and white pictures of IBM computers at the start of every chapter...WTH!! The only colour that exists in the book is red, which is used for titles/headings. A textbook is nothing without colours.

Cambridge is good, but it contains a lot of material that is not in the syllabus. (Bill Pender put in all the stuff he thought should be in the syllabus, not what actually is there.) The good thing about Cambridge is that the questions are graded by difficulty. One thing I really dislike about the Fitzpatrick textbooks is that they mix hard and easy questions up in any old order in the exercises. They also have their fair share of anachronisms cause they are from the 80's, too.

In WA a good portion of the state use Sadler textbooks for mainstream maths through to advanced maths in in yr11/12. The only colour in them is a distinctive plain coloured cover. The rest is black and white with few pictures (monochrome artwork), though there are some diagrams (also monochrome).

You don't need colour and pictures to learn maths.

that 2/3 unit maths SB jones and couchman are the most basic type of questions you can get (ie. fundamentals). Maths in focus is also too easy as well, fitzy has some errors on the answers but a good variety and cambridge is separated in 3 divisions, the basic revision, development and extension (for really keen students that plan to do 4U). I recommend past papers from other schools/especially your own school(most ruse students prepare by doing their past 10 years worth of papers) and also the past HSC exam papers when it gets to year 12.

Maths in Focus- an extremely good book if you don't understand the theorems as it explains all the details in a very easy to understand form, but I find that the questions that are in the sets are simplistic, as compared with our exams, maths in focus questions can be done in your sleep. But even then I highly recommend it as a reference book to help you understand the theorems and the concepts behind the questions.

Fitzpatrick- another very good book, with questions harder than Maths in Focus and the questions in the book can be expected to be similar to the HSC. There are numerous questions for each set which makes it easier to see the different varieties of each question. A drawback to the book is that in parts questions are mixed up in terms of their difficulty levels, so doing most of the set would be recommended.

Cambridge- a very good book, with questions divided into 3 sections based on their difficulty levels. This is an excellent book if you want the harder style examination questions, but be warned the last level of questions the extension section usually delves beyond the topic most of the time and usually are only attempted by Extension 2 maths students as these questions involve 4 unit maths concepts most of the time.

These are the three main textbooks used by most students at the 2/3 unit level.

However there are other different books such as Success One and Phoenix maths. These books are repositories of past hsc exam questions and contain sample past papers. These books are vital near the end of the course as it highlights the various ways questions can be construed by the examiners, and also to show the relative level of the hsc in terms of effort required. These books give their answers in a fully worked out format unlike all the other textbooks, this will help you if you are stuck with questions.

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