It's time to announce it, I suppose: I've withdrawn from the Ph. D. program in Mathematics.
Don't worry, I feel good about it. I might return one day, but for now, I'm ready to stop being a student for a tiny bit.
This decision slowly came to me over the winter break. During the break, I took two weeks off from thinking about mathematics. I was happier during the break than I had been in as long as I could remember. Studying math had become a very large source of stress in my life.
Let me give you some history. I started grad school in September 2007. The math department hopes you'll complete your first round of exams within two years, one year ideally. I haven't. I took two tests, failed them both. I know why I failed, but I just didn't ever seem to get good enough to fill in the gaps that caused me to fail.
This past fall, someone finally told me "you need to know real analysis." I really hadn't studied it. I even prided myself in avoiding it during my undergraduate classes. So I've been at a serious disadvantage. In October, I resolved to start teaching it to myself. But all that did was bring about more stress. It was more that I needed to study, in addition to the classes I was taking and the classes I was learning. I still believe I could do it if I wanted to. But I don't want to kill myself over it anymore.
So here's where I am now. I will still be teaching at New York City College of Technology, at least for Spring 2010. I'm in the process of looking for a second job. And I'm happy.
Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts
Monday, January 25, 2010
Wednesday, March 25, 2009
Studying Math
Grad school has been very difficult. I'm constantly learning how to "be" a mathematician.
I'll be frank, undergraduate classes were simple. Most of the work required was just getting the hang of whatever you were doing. This worked fabulously back at the University of Minnesota, Duluth. Especially in the philosophy program. I'd skim/read the material, doing my best to get the general impression. Then, I'd attend class and the professor would cement the general ideas in my mind. The details mattered only every once in a while. In fact, this process even worked backwards: I could attend class, get the general idea from the professor, then read the book and I'd be ready for an exam.
It doesn't work that way now. No matter how many times I read through a chapter, even if I use different books to get many different angles on a subject, it isn't enough. It's still difficult to follow lectures. I still have trouble completing the homework.
Today, I finally had the courage to ask one of my professors for advice. He said you've got to read a sentence, set the book aside, then play with it.
For example, here's the first sentence from Set Theory (Jech 2002).
Like most definitions in mathematics, I'd basically try to memorize it, and that's not necessarily wrong. But according to my professor, you've got to start testing the definition out. "What kind of property would work?" you might ask. "What about the property 'numbers less than 5'?" So, that means a set would be the numbers 0, 1, 2, 3, and 4. "Is that okay? Are numbers 'elements'?" I'm supposed to ask. "What if the property was not being equal to itself?" No number (or anything in the universe, for that matter) isn't equal to itself, so that would be an empty collection.
Of course this is the obvious thing to do. But it's hard in practice to do it. It's painful to stop reading a book every sentence, put the book aside and actually think. It reminds me of the saying "You can send them to college, but you can't make them think."
I suppose studying math is like exercising. Watching, listening and reading other people do mathematics is like watching someone on a treadmill. You don't gain anything unless you're on the treadmill yourself.
I sure hope I get the hang of it. I'm very proud of where I am and I want follow the path in front of me. It's just strange having to admit that I still need to improve my studying habits.
I'll be frank, undergraduate classes were simple. Most of the work required was just getting the hang of whatever you were doing. This worked fabulously back at the University of Minnesota, Duluth. Especially in the philosophy program. I'd skim/read the material, doing my best to get the general impression. Then, I'd attend class and the professor would cement the general ideas in my mind. The details mattered only every once in a while. In fact, this process even worked backwards: I could attend class, get the general idea from the professor, then read the book and I'd be ready for an exam.
It doesn't work that way now. No matter how many times I read through a chapter, even if I use different books to get many different angles on a subject, it isn't enough. It's still difficult to follow lectures. I still have trouble completing the homework.
Today, I finally had the courage to ask one of my professors for advice. He said you've got to read a sentence, set the book aside, then play with it.
For example, here's the first sentence from Set Theory (Jech 2002).
Intuitively, a set is a collection of all elements that satisfy a certain given property.
Like most definitions in mathematics, I'd basically try to memorize it, and that's not necessarily wrong. But according to my professor, you've got to start testing the definition out. "What kind of property would work?" you might ask. "What about the property 'numbers less than 5'?" So, that means a set would be the numbers 0, 1, 2, 3, and 4. "Is that okay? Are numbers 'elements'?" I'm supposed to ask. "What if the property was not being equal to itself?" No number (or anything in the universe, for that matter) isn't equal to itself, so that would be an empty collection.
Of course this is the obvious thing to do. But it's hard in practice to do it. It's painful to stop reading a book every sentence, put the book aside and actually think. It reminds me of the saying "You can send them to college, but you can't make them think."
I suppose studying math is like exercising. Watching, listening and reading other people do mathematics is like watching someone on a treadmill. You don't gain anything unless you're on the treadmill yourself.
I sure hope I get the hang of it. I'm very proud of where I am and I want follow the path in front of me. It's just strange having to admit that I still need to improve my studying habits.
Wednesday, March 4, 2009
But not 3 months!
Hello! It's been over two months since I last posted, and approaching three... but here I am! I'll do a little round up of what's going on, with further posting to come.
The Fall semester winded down with out much to comment on. My flight home for Christmas was canceled, getting me home on Christmas day. I still was able to see my family, but it's a shame our time was cut short.
I spent January studying and preparing for the next semester. I was actually treating it like a job. I'd go to school around 8 in the morning, stay there and study all day, then leave around 4 to 5pm. It was tough keeping focused, but being away from home helped a lot.
My semester started the last week of January. I'm enrolled in three classes:
1) Set Theory, a course about sets (believe it or not). This is the super-hard course of the semester. But in it, we started out studying "inaccessible cardinal numbers," numbers so big they become bigger than the theory that studies them. They're bigger than the numbers from 1 to infinity, they're bigger than all the decimal numbers between 0 and 1, and so on. They're actually called "Large."
2) Independent Study, a continuation of the work I did last semester on graphs. I only meet with my advisor every other week. When I do, I have to take the subway to City College, which is up in Harlem. From my apartment in Brooklyn, it's a 3 hour round trip. Needless to say, it's long. The worst part about it is according to Google Maps, I'm only traveling 7 miles each way.
3) Colloquium on College Teaching, a four week, 0 credit class about Academia. It's taught by Dr. Cahn, which is cool, because I used his Philosophy Anthology back at the University of Minnesota. I told him we always used to joke that you'd have to take passages in the book "Out of Cahn-text" (context). He actually enjoyed it, had never heard that before, and asked me to repeat it the next class. I guess everyone in Duluth, MN has strange humor. The class is actually over now. I really enjoyed it. Despite the name, it discussed a lot of useful information, like who the Provost is at a college, what needs to be done to get tenure, etc.
As for my teaching, I'm teaching two courses at night, Mondays and Wednesdays. One runs from 6pm to 7:40pm, the other from 8pm to 9:40pm. I've taught this course twice before, so it's been straight forward. I'm surprised how quiet the College gets at night. I'm the only math professor teaching the 8pm shift. The 6pm class as lively as normal, but the 8pm class gets very quiet.
Actually, today is the day of the first exam. To tell the truth, I haven't written it yet. So I better get writing.
To come: Weather, Livia, Brooklyn, Alicia, and much, much more!
The Fall semester winded down with out much to comment on. My flight home for Christmas was canceled, getting me home on Christmas day. I still was able to see my family, but it's a shame our time was cut short.
I spent January studying and preparing for the next semester. I was actually treating it like a job. I'd go to school around 8 in the morning, stay there and study all day, then leave around 4 to 5pm. It was tough keeping focused, but being away from home helped a lot.
My semester started the last week of January. I'm enrolled in three classes:
1) Set Theory, a course about sets (believe it or not). This is the super-hard course of the semester. But in it, we started out studying "inaccessible cardinal numbers," numbers so big they become bigger than the theory that studies them. They're bigger than the numbers from 1 to infinity, they're bigger than all the decimal numbers between 0 and 1, and so on. They're actually called "Large."
2) Independent Study, a continuation of the work I did last semester on graphs. I only meet with my advisor every other week. When I do, I have to take the subway to City College, which is up in Harlem. From my apartment in Brooklyn, it's a 3 hour round trip. Needless to say, it's long. The worst part about it is according to Google Maps, I'm only traveling 7 miles each way.
3) Colloquium on College Teaching, a four week, 0 credit class about Academia. It's taught by Dr. Cahn, which is cool, because I used his Philosophy Anthology back at the University of Minnesota. I told him we always used to joke that you'd have to take passages in the book "Out of Cahn-text" (context). He actually enjoyed it, had never heard that before, and asked me to repeat it the next class. I guess everyone in Duluth, MN has strange humor. The class is actually over now. I really enjoyed it. Despite the name, it discussed a lot of useful information, like who the Provost is at a college, what needs to be done to get tenure, etc.
As for my teaching, I'm teaching two courses at night, Mondays and Wednesdays. One runs from 6pm to 7:40pm, the other from 8pm to 9:40pm. I've taught this course twice before, so it's been straight forward. I'm surprised how quiet the College gets at night. I'm the only math professor teaching the 8pm shift. The 6pm class as lively as normal, but the 8pm class gets very quiet.
Actually, today is the day of the first exam. To tell the truth, I haven't written it yet. So I better get writing.
To come: Weather, Livia, Brooklyn, Alicia, and much, much more!
Wednesday, August 13, 2008
Schools out for the summer
I finished teaching today!
I've been teaching a summer session of Developmental Mathematics (read: pre-college math). It met Monday - Thursday, 8:30 to 12:15ish. It has been all prep for the final and the ACT Compass exam, an exam students must pass to enter college math. Thus, all my students had taken the ACT Compass exam and failed it, meaning this course was prep work for it.
I started out with 18 students and it dropped down to 16 by the end. Of those 16 students who completed the class, three passed.
Yes, three. Today I failed 13 students. Ouch.
I talked to the head of the math department, as I was concerned. He said it was mostly the luck of the draw. He personally had taught a class where only one person passed. Still, I've been upset today. I feel like I failed as a professor.
I know that isn't true. I know I did as much as I could. Because I corrected the final exams, I know that the mistakes made were covered. Several mistakes made I specifically warned the students that "Students always make these mistakes. Tests will ask you this. Don't be one of those students!" For instance:
-1 - 6
The answer is -7. Most of my students thought it was 5 or -5.
Oh well. I did pass three students. They did a great job, and I am sure they'll pass the ACT now. As for me, I'm just going to leave it behind and relax in Minnesota this weekend.
I've been teaching a summer session of Developmental Mathematics (read: pre-college math). It met Monday - Thursday, 8:30 to 12:15ish. It has been all prep for the final and the ACT Compass exam, an exam students must pass to enter college math. Thus, all my students had taken the ACT Compass exam and failed it, meaning this course was prep work for it.
I started out with 18 students and it dropped down to 16 by the end. Of those 16 students who completed the class, three passed.
Yes, three. Today I failed 13 students. Ouch.
I talked to the head of the math department, as I was concerned. He said it was mostly the luck of the draw. He personally had taught a class where only one person passed. Still, I've been upset today. I feel like I failed as a professor.
I know that isn't true. I know I did as much as I could. Because I corrected the final exams, I know that the mistakes made were covered. Several mistakes made I specifically warned the students that "Students always make these mistakes. Tests will ask you this. Don't be one of those students!" For instance:
-1 - 6
The answer is -7. Most of my students thought it was 5 or -5.
Oh well. I did pass three students. They did a great job, and I am sure they'll pass the ACT now. As for me, I'm just going to leave it behind and relax in Minnesota this weekend.
Monday, July 14, 2008
Teaching
Well, it is Tuesday. Only three more days of work for me. I've finally started getting used to the 3Hr 45Min classes.
As you may recall, I'm teaching at New York City College of Technology this summer, teaching a class for students just entering the college out of High School. These are students who got lower than 18 on the Math ACT exam, which is required to enter the "for credit" math classes. CUNY (City University of New York) offers the class I am teaching for free to give these students a chance to get back into regular math curriculum.
The class starts at 8:30 and runs until 12:15, so it is something of a marathon. The hardest part of teaching so far has been keeping the students interested. One way I've done it has been bringing in candy. I know it is silly, but it does seem to wake the students up when I am throwing a mini snickers at them. Alicia gave me the idea, saying one of her Law Professors did it and it was very effective. I usually give the candy away if a student catches one of my mistakes, or answers a trivia question I'll occationally throw out.
As for the math curriculum, I'm trying something different. I'm teaching them about polynomials without using subtraction or division. I'm hoping it will simplify things.
I'm giving an exam every single Thursday, so I've already returned one. The average was 86, which is pretty good. There were students still getting 62, and I'd love to reach them. I just hope the exam wasn't too easy.
Of course, the hardest part so far has been waking up. The subway ride is only about half an hour (CityTech is in Brooklyn), but I can't be late as I'm the professor. So I usually leave the apartment by 7:30. As a result, I'm awake around 6:30. Sunday night darn near killed me though. I couldn't get asleep until about 1:30am, so waking up at 6:30 was harsh. I ended up going to bed around 9:30 last night, thus the reason I'm up at 5am today. Oh well!
As you may recall, I'm teaching at New York City College of Technology this summer, teaching a class for students just entering the college out of High School. These are students who got lower than 18 on the Math ACT exam, which is required to enter the "for credit" math classes. CUNY (City University of New York) offers the class I am teaching for free to give these students a chance to get back into regular math curriculum.
The class starts at 8:30 and runs until 12:15, so it is something of a marathon. The hardest part of teaching so far has been keeping the students interested. One way I've done it has been bringing in candy. I know it is silly, but it does seem to wake the students up when I am throwing a mini snickers at them. Alicia gave me the idea, saying one of her Law Professors did it and it was very effective. I usually give the candy away if a student catches one of my mistakes, or answers a trivia question I'll occationally throw out.
As for the math curriculum, I'm trying something different. I'm teaching them about polynomials without using subtraction or division. I'm hoping it will simplify things.
I'm giving an exam every single Thursday, so I've already returned one. The average was 86, which is pretty good. There were students still getting 62, and I'd love to reach them. I just hope the exam wasn't too easy.
Of course, the hardest part so far has been waking up. The subway ride is only about half an hour (CityTech is in Brooklyn), but I can't be late as I'm the professor. So I usually leave the apartment by 7:30. As a result, I'm awake around 6:30. Sunday night darn near killed me though. I couldn't get asleep until about 1:30am, so waking up at 6:30 was harsh. I ended up going to bed around 9:30 last night, thus the reason I'm up at 5am today. Oh well!
Thursday, June 26, 2008
Sifting through the Summer
Well, it hasn't been a month yet, but might as well have. I teach in about a week and a half, so I've begun preparing. The course I'm teaching is officially called "Elementary Algebra with Basic Mathematics Review." It begins Monday, July 7th, and runs through August 14th. It will be intense. It meets Monday, Tuesday, Wednesday, and Thursday from 8:30am until 12:15, 12:30pm on Thursdays. That makes 15 1/2 hours a week. I'm excited, as I should be able to expect the best from these students, having them for so long. There is definitely the potential for boredom, but that should be avoidable as long as I don't lecture the full 3:45 of the lecture. And after teaching a Friday class for 3:20, I certainly don't intend to.
I'm happy that there is this deadline for work that needs doing, as I'm not nearly as good at this self-discipline as I thought I would be. I haven't completely dropped the ball, and I'm rather proud of my work in Graph Theory, but it has been hard to keep up a pattern.
Take, for instance, the last two days. I've been on a Food Network kick. Thus, cooking has been in the forefront of my mind. Alton Brown's Good Eats had an entire episode devoted to the popover recipe, so I had to try it. I bought popover tins, and I've made them twice since Tuesday. They are extremely easy. I've got the recipe memorized myself. 1 Cup Whole Milk, 1 Tbsp Butter, 1/2 Tsp Kosher Salt, 1 Cup All Purpose Flour, 2 Eggs: all in a blender for 30 seconds, then in the tins for 40 minutes under 400 degree heat. What is so appealing is I understand all of it. Apparently, the blending makes lots of bubbles of tiny bubbles. The eggs under heat hold the outer layer intact, so the tiny bubbles turn to steam, which mix in the batter to turn into a giant bubble by the time 40 minutes has elapsed. So when the popovers are done, you just poke a hole in the top to let the steam out, and you've got dinner roll style cups to fill with anything, or just eat plain. Tuesday night, I filled them with teriyaki chicken and onions, yesterday I filled them with the fruit that we had leftover in the fridge. They are so easy. The only real challenge is having whole milk in the house.
Speaking of Alton Brown, Alicia and I bought his book, I'm Just Here For The Food. Great book. It's a cookbook, but the recipes are built up to with an explanation of the cooking methods or the ingredients involved. He explains that a recipe is like a friend drawing you a map for directions. If you follow the directions (recipe), you'll get where you want to go. But if something goes wrong, such as a tree is blocking a road (or cheap frying pans effect cooking time), you're in the dark. That is exactly how I've always felt about recipes: in the dark. The only ingredients I actually feel familiar with are chicken, onions, and green peppers (thanks to salsa and stir fry). Sure, I've used mushrooms or paprika before in a recipe, but I know very little about the ins and outs of the ingredients.
Basically, I've been on a cooking binge as of late. Last night, I seared scallops (very easy!) and tried my hand at ratatouille (big failure, I think I over cooked it). Previously, I made Chipotle Cashew Chicken (below) and grilled Pineapple Kabobs (above) along with regular kabobs.
I'm happy that there is this deadline for work that needs doing, as I'm not nearly as good at this self-discipline as I thought I would be. I haven't completely dropped the ball, and I'm rather proud of my work in Graph Theory, but it has been hard to keep up a pattern.
Take, for instance, the last two days. I've been on a Food Network kick. Thus, cooking has been in the forefront of my mind. Alton Brown's Good Eats had an entire episode devoted to the popover recipe, so I had to try it. I bought popover tins, and I've made them twice since Tuesday. They are extremely easy. I've got the recipe memorized myself. 1 Cup Whole Milk, 1 Tbsp Butter, 1/2 Tsp Kosher Salt, 1 Cup All Purpose Flour, 2 Eggs: all in a blender for 30 seconds, then in the tins for 40 minutes under 400 degree heat. What is so appealing is I understand all of it. Apparently, the blending makes lots of bubbles of tiny bubbles. The eggs under heat hold the outer layer intact, so the tiny bubbles turn to steam, which mix in the batter to turn into a giant bubble by the time 40 minutes has elapsed. So when the popovers are done, you just poke a hole in the top to let the steam out, and you've got dinner roll style cups to fill with anything, or just eat plain. Tuesday night, I filled them with teriyaki chicken and onions, yesterday I filled them with the fruit that we had leftover in the fridge. They are so easy. The only real challenge is having whole milk in the house.
Speaking of Alton Brown, Alicia and I bought his book, I'm Just Here For The Food. Great book. It's a cookbook, but the recipes are built up to with an explanation of the cooking methods or the ingredients involved. He explains that a recipe is like a friend drawing you a map for directions. If you follow the directions (recipe), you'll get where you want to go. But if something goes wrong, such as a tree is blocking a road (or cheap frying pans effect cooking time), you're in the dark. That is exactly how I've always felt about recipes: in the dark. The only ingredients I actually feel familiar with are chicken, onions, and green peppers (thanks to salsa and stir fry). Sure, I've used mushrooms or paprika before in a recipe, but I know very little about the ins and outs of the ingredients.
Basically, I've been on a cooking binge as of late. Last night, I seared scallops (very easy!) and tried my hand at ratatouille (big failure, I think I over cooked it). Previously, I made Chipotle Cashew Chicken (below) and grilled Pineapple Kabobs (above) along with regular kabobs.
But with too much cooking comes too many dishes. I need a break. So tonight we're ordering out. Pizza I think. Yay!
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