Online Mathematics Degrees
Last week, I received an email from a reader regarding the online mathematics program at the University of Illinois in Springfield. I wasn’t familiar with the program and have started taking a closer look. One of the questions that was asked by that reader was what sort of things should he be looking for in an online mathematics degree. To my knowledge the are very few fully online bachelor’s degrees IN MATHEMATICS available at this point. However, with technology advancing at its current rate, the barriers to such a program will be virtually gone in the next few years.
So what exactly are the barriers to an online mathematics degree? I have a few ideas but I’m interested in what other folks are thinking, so I am scoping out the blogosphere and reading as many articles as I can get my hands on. If you have any recommendations, I’d love to hear them.
Even as an online mathematics instructor, I still believe that the majority (vast majority, in fact) are better off in a face-to-face setting than online. Now, the only course I teach is a College Algebra course that is required for all bachelor’s degrees at Wayland. None of my online students are math majors or will become math majors. I’m not discouraging them, but they are all attending our external campuses where we don’t offer the full program in mathematics, for lack of demand, primarily. So these students range from a few students straight out of high school to the majority of which are adult learners returning to school. About half of the students I have are truly motivated enough to do the self-teaching necessary to learn the material through the online medium, but the communication barrier still looms as the largest hurdle to success for almost all of the students.
To answer the reader’s question, “What should I be looking for in [an online mathematics program]?”, I replied the following:
While many Universities have moved to put several undergraduate courses online such as College Algebra, Pre-Calculus and Calculus. There is much less available in terms of the upper level courses that involve abstract mathematics and proof techniques.
Most of all, abstract mathematics needs a high level of communication and interaction during the learning process. Conveying ideas in those courses are very challenging using the online medium. I think the courses need to have both asynchronous elements and synchronous elements, meaning that there will be times you work on your own time schedule and others that you interact with your class or your professor with immediate feedback. That's probably the biggest thing. You also need the benefit of interacting with fellow students in the program. A cohort of learners is extremely important during the process or mastering abstract-level mathematics.
What else would be important for mathematics degree to be completely online or is it even possible?
But Tell Me, What of Your Teachers
(Presented by Dr. Wallace Davis at the Centennial Heritage Chapel at Wayland Baptist University, with possibly original elements and some from anonymous sources)
While some Universities may boast of their age, of their ivied walls,
Of their great endowments, their marble halls,
Of their vast curricular scope and reach,
And of all the wonderful things they teachTell me, tell me of their teachers
For no printed word nor spoken plea
Can teach a heart what men should be,
Not all the books on all the shelves.
Oh no, it’s what the teachers are themselves.
Another Number Puzzle
I know some of you who read this blog also read 360 but the sequence posted there today was too good to not pass along:
Puzzle: Identify the next term in the sequence
1, 11, 21, 1211, 111221, 312211, 13112221, . . .
[HINT: Read the digits aloud. The sequence is aural/visual and not numeric.]
I’ll post the answer tomorrow or the next day.
Finished Reading: Pillars of the Earth
Just finished a book I got myself for Christmas. Actually, it was from Lori but she had me pick it out.
Pillars of the Earth by Ken Follett.
I really enjoyed reading it and would recommend it, heartily.
I’m reading a biography of Alan Turing next.
Alan Turing: The Enigma by Andrew Hodges.
I take it back!
So far since the beginning of the week , I have received no less than four messages claiming to have attachments that did not. Within seconds of receiving them, a follow-up email arrives confessing the stupidity, idiocy, or moron-itude of the sender plus the previously promised attachment. I point no fingers as I am as guilty in this matter as anyone else.
Worse yet are those “Reply-to-all” instead of “Reply” mistakes. Even worse is the Reply instead of Forward to. I recall one time receiving an answer to a question from the Facilities Manager here on campus (my land-lord, basically) which I did not like. Instead of forwarding to my wife my response of “Ugh!”, I replied that back to him. Nice move, Einstein.
So, here’s a recommendation to all you happy clickers that let the send button do the talking when you’re not quite ready:
Email Delivery Delay in Outlook 2003/2007:
This allows you to double check and re-think sending your email even after hitting the send button. It causes your email be held for a specified number of minutes after hitting send.
- On the Tools menu, click Rules and Alerts, and then click New Rule.
- Select Start from a blank rule.
- In the Step 1: Select when messages should be checked box, click Check messages after sending, and then click Next.
- In the Step 1: Select condition(s) list, select any options you want, and then click Next.
If you do not select any check boxes, a confirmation dialog box appears. Clicking Yes applies this rule to all messages you send.
- In the Step 1: Select action(s) list, select defer delivery by a number of minutes. Delivery can be delayed up to two hours.
- In the Step 2: Edit the rule description (click on an underlined value) box, click the underlined phrase a number of and enter the number of minutes you want messages held before sending.
- Click OK, and then click Next.
- Select any exceptions, and then click Next.
- In the Step 1: Specify a name for this rule box, type a name for the rule.
- Click Finish.
Forgotten Attachment Detector in Gmail
For Gmail there is an experimental feature that detects from the wording of your message that you intended to attach a file but did not. It pops up a warning if it thinks you meant to attach something.
To enable this feature, go under the Google Labs section of the Settings page in Gmail. Scroll down to “Forgotten Attachment Detector” and select Enable. Then click “Save Changes” at the bottom.
I just turned it on for the first time and ran a few tests on the way I might say that I have an attachment. For example:
- “I have attached a file” – works
- “see attached” - works
- “see attachment”- works
- “Attachment” as subject line – did not work
- “Here is the file I mentioned” – did not work
Not bad. It’s worth having running in the background.
Mail Goggles in Gmail
For those emails that you send late in the evening or over the weekend when your head isn’t in the right mindset to respond to some naysayer at work, wouldn’t be nice of something stopped before you vented all over them. How about having to work out 5 arithmetic problems before you send? That would give you time to reconsider what you have written.
There’s another experimental feature in Gmail that does just that called Mail Goggles. I don’t use this one but I’ve played with it. You can control the difficulty and set a schedule for when this will interrupt your sending.
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I have yet to discover a way to delay the delivery of an email sent through the Gmail web interface. If anyone knows how, I’m certainly interested.
Another Calculus Limerick
I love a good math limerick. And, no, “Nantucket” is never a destination for some mathematician in a good math limerick. Here’s a new one I discovered online:
For the laymen,
The integral sec y dy -> (read as “seek y dee y”)
From zero to one-sixth of pi
Is the log to base e
Of the square-root of three
Times the sixty fourth power of i.
This rivals my favorite limerick of all time. And I can’t talk about limericks without repeating it for you:
![\displaystyle \int_1^{\sqrt[3]{3}} z^2 \, dz \cdot \cos \left( \frac{3\pi}{9} \right) = \ln \sqrt[3]{e}](/latexrender/pictures/6a45cec14ae80c3fcbde6dc54e134cf7.png "\displaystyle \int_1^{\sqrt[3]{3}} z^2 \, dz \cdot \cos \left( \frac{3\pi}{9} \right) = \ln \sqrt[3]{e}")
Again, for the unconverted,
The integral z-squared dz
From one to the cube root of 3
Times the cosine
Of three pi over nine
Is the log of the cube root of e.
“It’s gold, Jerry! Gold!”
Recent Coding Projects
There have been a number of interesting projects I’ve been asked to work on over the course of the last few weeks. They all involve writing a little code and so I want to document some of those projects here. They are not math related but my interests are broader than just numerical analysis and bioinformatics. Plus, in the age where “google” has become a verb, I attract occasional visitors to this site looking for solutions to problems that I have solved for myself, like repairing a broken headphone jack or enabling wifi on a misbehaving smart phone.
Consolidating data in multiple excel workbooks
Consider the case where you might have a large set of excel spreadsheets spread across a number of different workbooks. If you want to consolidate, merge, extract or just combine data, there isn’t really an ideal tool for doing this. There is a “Consolidate data” function in excel but it isn’t suited to large numbers of files because it becomes tedious opening and selecting the range over and over. While many Excel gurus might have other solutions, I decided to go the macro route.
As in most cases, I was able to find resources available online that would accomplish something similar to what I wanted.
Goal #1:
Take all the data (used range of cells) in all the worksheets in all the workbooks in a specified directory and combine them into a single sheet (or several sheets in the same workbook if they don’t fit)
Is God a Mathematician?
"The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve".
from The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Nobel Laureate Eugene Wigner (1960)
An article by the author Mario Livio, who recently wrote the book Is God a Mathematician?, appeared in Plug Magazine in December. After reading the article, I immediately added his book to my reading list.
Essentially, the question that both the article and book address is whether or not the effectiveness of mathematics to model and predict natural events is unusual relative to other historical attempts to do so. And if so, why does mathematics possess this unreasonable effectiveness in the natural sciences?
Livio categorizes the effectiveness of mathematics into two facets, labeling them as active and passive. By active, he is referring to those instances where scientists actively use mathematics to “light their path” through complexity of natural phenomena. They develop new models and use these models to answer questions about the world around them.
Even more interesting to me is the second facet. In the passive sense, the effectiveness of mathematics is demonstrated when mathematics in its purest sense is developed simply for the sake of mathematics but eventually becomes a very powerful model for an aspect of nature. Pure mathematics studies patterns and structures within the mathematical objects themselves, with no concern for the applicability of the mathematics to the real world. In fact, a true pure mathematician would see a physical, real-world application of their theorem as something that takes away from the purity and beauty of mathematics.
While I’m sure his book (that I’ve not yet read) contains a number of examples of these, the article mentioned above provides the example of knot theory. “Knots, and especially maritime knots, enjoy a long history of legends and fanciful names such as ‘Englishman's tie,’ ‘hangman's knot,’ and ‘cat's paw’.” As Livio tells it,
Knots became the subject of serious scientific investigation when in the 1860s the English physicist William Thomson (better known today as Lord Kelvin) proposed that atoms were in fact knotted tubes of ether (that mysterious substance that was supposed to permeate space). In order to be able to develop something like a periodic table of the elements, Thomson had to be able to classify knots—find out which different knots are possible.
As we all know, the existence ether was later disproven, but an entire theory of mathematics had been born out of this. The concept of a mathematical knot developed, theorems for classification of these knots were proven and knot theory continued as area of interest to many pure mathematicians.
The surprising part is when physicists in the late 20th century discovered a connection between aspects of knot theory and the burgeoning field of string theory.
In particular, string theorists Hirosi Ooguri and Cumrun Vafa discovered that the number of complex topological structures that are formed when many strings interact is related to the Jones polynomial. [The Jones polynomial is used in the classifications of knot variations]
This connection is completely unexpected and most surprising. In a particular twist, this application of a mathematical idea was once developed for a theory about the fundamental substance of all matter, namely ether, which was eventually discarded. It returns much later to explain a great deal about today’s modern theory about the fundamental substance of all matter.
Now for my input. GOD IS A MATHEMATICIAN! As I tell all of my students, one of the primary reasons I study mathematics and call myself a mathematician is that it has been established as the language of science and science is, at its very core, the study of God’s creation. Due to the “unreasonable effectiveness” of mathematics, its clear to me that God’s nature has a very strong mathematical component. That God follows patterns that are detectable to his creatures tells me at least two things: (1) God is personal and wants us to discover him, and (2) God is faithful to follow his established pattern. He is immutable and unchanging. The effectiveness of mathematics by no means proves these traits of God, but from my viewpoint as a man of faith and a mathematician, it serves as very strong evidence for them.
Twitter summaries are history
Just a short post here to let you know that I am discontinuing the “Twitter Updates of the Week”. For the last few weeks, I have had a plug-in for this blog post all of my Twitter posts, aka “tweets”, for the previous week. Since I have Twitter piped into my facebook status, most of the friend of this blog were getting a double or even triple dose. I felt it cluttered up the blog and misrepresented the blog’s primary purpose. So, they’re history.
If you’re interested in keeping up with the life and trials of the Christian Mathematician, you can follow me on Twitter (http://twitter.com/splineguy) or you can just take a gander to the right of this post in the sidebar where you’ll see my latest status update.
By its very nature, this blog is a work in progress. What I intend for it to be changes from week to week. There are spurts of activity and the lulls. I appreciate those who continue to follow and I hope that every once in a while something of interest tickles your fancy, as they say.
Number Puzzle #2 Solution
I’m embarrassed by the fact that I have 3 weeks of Twitter updates cluttering the first page of this blog. That means, that I’ve gone without blogging for at least two weeks. I was trying to get on a roll with the number puzzles. I have a backlog of some interesting links and topics in my bookmarks list so.
Back on December 8, I posted the following problem:
Form a number from the digits 0 to 9 such that the first digit is divisible by one, the first two digits form a number that is divisible by two, the first three digits form a number that is divisible by three, and so forth.
As was pointed out by one of the commenters, this was ambiguous because I wasn’t clear if I meant first from the left or first from the right. I actually meant from the left but the problem can be solved either way.
For the intended question, the solution is 3816547290.
Here’s a solution given by Jenning Y. Seto.:
Let each of the digits in the number be represented by a letter
so that the number is: abcdefghijFirst of all, we can see that ab/2, abcd/4, abcdef/6, abcdefgh/8,
and abcdefghij/10 are integers, therefore, b, d, f, h, and j are all
even. Since we only have five even digits (0, 2, 4, 6, and 8), a, c,
e, g, and i are all odd digits. Furthermore, knowing that certain
parts of the number are divisible by certain numbers gives us the
following constraints:1. a/1 is an integer tells us nothing.
2. ab/2 is an integer tells us that b is even.
3. abc/3 is an integer tells us that (a+b+c)/3 is an integer.
4. abcd/4 is an integer tells us that cd/4 is also an integer and d is even. Since c is odd, d must be 2 or 6.
5. abcde/5 is an integer tells us that e MUST be 5.
6. abcdef/6 is an integer tells us that (a+b+c+d+e+f)/3 is an integer and that f is even.
7. abcdefg/7 is an integer can be used later.
8. abcdefgh/8 is an integer tells us that fgh/8 is an integer and h must be 2 or 6 since g is odd.
9. abcdefghi/9 is an integer tells us that (a+b+c+d+e+f+g+h+i)/9 is an integer.
10. abcdefghij/10 is an integer tells us that j MUST be 0.Constraint 9 tells us nothing since constraint 10 states that j is 0,
and the sum of the remaining digits is divisible by nine.From constraints 4 and 5, the only possible values for the digits
d and e arede = 25 or 65.
Combining constraints 3 and 6 we see that (d+e+f)/3 must be
an integer and that f is even. Thus,de = 25 implies f = 8.
de = 65 implies f = 4.
This gives us two possible cases:
def = 258 or 654.
Using constraint 8, we can see that
def = 258 implies gh = 16 or 96.
def = 654 implies gh = 32 or 72.
Now we have four possibilities that satisfy constraints 4, 5, 6,
and 8:defgh = 25816, 25896, 65432, or 65472.
Notice that in all 4 cases, 2 and 6 are used. Thus b = 4 or 8.
Now using constraint 3 with the above constraints leaves us with
a number of possibilities for abc:abc = 147, 183, 189, 381, 741, 789, 981, or 987.
Even with the above constraints, this gives us ten possibilities
for the first eight digits:abcdefgh = 14725896, 18365472, 18965432, 18965472,
38165472, 74125696, 78965432, 98165432, 98165472, or 98765432.However, we can use constraint 7, and see that only
abcdefg = 3816547 is divisible by 7.
Thus the final answer is 3816547290. Furthermore, this is a unique
answer.