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Subsections
What do research mathematicians do? Most Canadian high school students do not know. What is even more troubling is that most Canadian high school mathematics teachers do not know either.
The answer needs to come directly from research mathematicians. Research mathematicians understandably are concerned with their research. Nevertheless, without the Gretzky's of math directly participating in answering the question it will always remain an open question to Canadian high school students.
One suggestion is to form a travelling team of research mathematicians analogous to the Legends of Hockey tour. They would travel Canada inspiring high school students directly by giving public lectures at public schools and establishing contacts with high school mathematics teachers in person.
One problem is that this will take a lot of work and travel energy on their part and I don't think the mathematicians still researching will be keen participants. So, what can be done?
Many high school students watch TV. The Discovery channel
I would like to see research mathematicians interviewed on the Discovery channel. -Ed.
Despite the fact that the UNBC Math Department is underfunded, understaffed and shows no signs of improving in these areas, I believe I could not have received a better undergraduate education anywhere else.
The shortage of staff is a definite problem, which is added to by the high turnover. In my view, there are not enough professors to teach the required courses, and the professors generally end up teaching a wide variety of different courses. This is difficult on both students and faculty. I was fortunate that we had a number theorist, Dr. Chris Pinner, for two years, as this is the field of mathematics I intend to pursue. I believe many students do not gain as much as they could due to the lack of a professor in their field of interest.
It is not hard to argue however, that the faculty we do have make up for any problem the department has. Many of the professors are very dedicated to their students and give them opportunities they would not have elsewhere. I have been a TA since the beginning of my second year (undergrad), as well as having the opportunity to assist Dr. Pinner in his research. (See my Lagrange Spectrum Calculator http://ctl.unbc.ca/CMS/LSC). This kind of experience is invaluable as I intend to become a university professor myself one day. Many other students have had this same opportunity with a variety of professors. On top of this, all of the professors I have had are excellent teachers and really demonstrate their love for mathematics. The UNBC math professors do not just give notes and tests, they give their students support, encouragement, experience, and an appreciation for the wonderful world of math.
Overall, I think the UNBC Math Department definitely has room for improvement, which is not so surprising since it is such a young university. The faults of the department, however, are greatly overshadowed by the staff and faculty in it. I am very fortunate to have been a part of this department and when I leave for graduate school I will be very proud to say that I received my undergraduate degree from UNBC.
Reviewed by Andy Culham, ajculham@ucalgary.ca.
This book is designed to serve as a text for a senior undergraduate linear algebra course. The first three chapters (vector spaces, matrices, and liner mappings) briefly cover material that should have become second nature to any senior undergraduate student. The book then proceeds to very quickly cover much more advanced topics such as scalar products, determinants, and eigenvalues/eigenvectors. While these topics are covered in a junior course, they are approached much more rigorously here. The proofs of theorems are often brief and lack in detail. While there are exercises provided at the end of each section, there are no solutions or hints provided anywhere in the text, nor is there a solution manual available for purchase. Many undergraduates will find this quite frustrating and may have to resort to purchasing a supplementary text which includes problems with solutions. While this book is efficient and moderately priced, the content and presentation is less than sufficient for most undergraduates.
O'Neill, B. Elementary Differential Geometry-2nd edition. Academic Press, San Diego, CA, 1997.
Reviewed by Dan Wolczuk, wolczu0@unbc.ca.
To be to the point, I am not very impressed by this text book. The two main problems I have with this book are that some definitions and formulas are hidden amongst regular text, and that there is a major lack of descriptive examples. If it were not for the former problem I would believe that this would make a good reference book, but unfortunately you cannot find all of the necessary definitions and theorems by merely scanning the pages. The lack of examples makes the textbook fairly difficult to learn from as the explanations of concepts and proofs of theorems are not always complete. The questions at the end of each chapter are the only part of the book I have to commend. They do an excellent job of ensuring an understanding of the material from the previous chapters. For example, in doing questions from Chapter 4, if you do not have a good grasp of the previous three chapters you will find the questions quite difficult. However, with a good understanding of the necessary material many of the questions are quite trivial. Overall I am not at all a fan of this book, although I have definitely learned the necessary material from it, so it cannot be all that bad.
Ross, Kenneth A. Elementary Analysis: The Theory of Calculus. Springer-Verlag, 1980.
Reviewed by Raymond Cheng, kwrcheng@ucalgary.ca.
The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for non-math majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with non-essential talk. It gets into the material right away. The proofs have been carefully chosen so that they're as simple and as elegant as possible. Topology is treated in optional sections, and the focus of the book is sequences. Indeed, the treatment of sequences is very thorough. Also, many notions are also defined in terms of sequences. However, proof that this definition and the usual delta-epsilon definition are equivalent is given. The style of writing is clear, concise, and avoids unnecessary discussion. Proofs are given out in full and are seldom left to the readers as an exercise. In keeping with the style of this book, historical facts and references are not provided. I think this book should be a must-have for all math undergrads. Pi in the Sky. The Pacific Institute for the Mathematical Sciences, June 2000. Available at (opens in new window): http://www.pims.math.ca/pi
Reviewed by Raymond Cheng, kwrcheng@ucalgary.ca.
Pi in the Sky is a semiannual mathematical magazine targeted at junior and senior high school students and educators. However, I find that some of the content might be too advanced and the magazine as a whole might be more appropriate for undergraduates. There are nearly ten articles in this periodic publication along with jokes, comics and other interesting materials. As stated in the publication, ``This journal is devoted to cultivating mathematical reasoning and problem-solving skills, to prepare students for the challenges of the high-technology era." The magazine is professionally produced and if you plan to read it from cover to cover, it will set you back a couple of hours. There are some interesting math questions at the end of the magazine, and the reader is invited to submit solutions. Overall, I think this journal is a good read for all math undergraduate students as well as advanced high school students.
If you have an event or deadline which you would like to include, visit our website and drop our webmaster Andrew Irwin a line. Andrew J. Irwin 2001-03-19
Math talk
Editorial
Time to show initiativeWhat do research mathematicians do? Most Canadian high school students do not know. What is even more troubling is that most Canadian high school mathematics teachers do not know either.
The answer needs to come directly from research mathematicians. Research mathematicians understandably are concerned with their research. Nevertheless, without the Gretzky's of math directly participating in answering the question it will always remain an open question to Canadian high school students.
One suggestion is to form a travelling team of research mathematicians analogous to the Legends of Hockey tour. They would travel Canada inspiring high school students directly by giving public lectures at public schools and establishing contacts with high school mathematics teachers in person.
One problem is that this will take a lot of work and travel energy on their part and I don't think the mathematicians still researching will be keen participants. So, what can be done?
Many high school students watch TV. The Discovery channel
http://exn.ca/@discovery.ca
is giving nice profiles on biologists, chemists, physicists, astronomers,
anthropologists, archaeologists, and so on. The point is that they have
reduced mathematics to a Numbers Game past time. Personally,
I would love to be updated on new mathematical discoveries and more
importantly, how such discoveries were made.
I would like to see research mathematicians interviewed on the Discovery channel. -Ed.
Opinions/Commentary
On the UNBC Math Department by Dan Wolczuk wolczu0@unbc.ca.Despite the fact that the UNBC Math Department is underfunded, understaffed and shows no signs of improving in these areas, I believe I could not have received a better undergraduate education anywhere else.
The shortage of staff is a definite problem, which is added to by the high turnover. In my view, there are not enough professors to teach the required courses, and the professors generally end up teaching a wide variety of different courses. This is difficult on both students and faculty. I was fortunate that we had a number theorist, Dr. Chris Pinner, for two years, as this is the field of mathematics I intend to pursue. I believe many students do not gain as much as they could due to the lack of a professor in their field of interest.
It is not hard to argue however, that the faculty we do have make up for any problem the department has. Many of the professors are very dedicated to their students and give them opportunities they would not have elsewhere. I have been a TA since the beginning of my second year (undergrad), as well as having the opportunity to assist Dr. Pinner in his research. (See my Lagrange Spectrum Calculator http://ctl.unbc.ca/CMS/LSC). This kind of experience is invaluable as I intend to become a university professor myself one day. Many other students have had this same opportunity with a variety of professors. On top of this, all of the professors I have had are excellent teachers and really demonstrate their love for mathematics. The UNBC math professors do not just give notes and tests, they give their students support, encouragement, experience, and an appreciation for the wonderful world of math.
Overall, I think the UNBC Math Department definitely has room for improvement, which is not so surprising since it is such a young university. The faults of the department, however, are greatly overshadowed by the staff and faculty in it. I am very fortunate to have been a part of this department and when I leave for graduate school I will be very proud to say that I received my undergraduate degree from UNBC.
Book Review
Lang, S. Linear Algebra-3rd edition. Springer-Verlag, 1989.Reviewed by Andy Culham, ajculham@ucalgary.ca.
This book is designed to serve as a text for a senior undergraduate linear algebra course. The first three chapters (vector spaces, matrices, and liner mappings) briefly cover material that should have become second nature to any senior undergraduate student. The book then proceeds to very quickly cover much more advanced topics such as scalar products, determinants, and eigenvalues/eigenvectors. While these topics are covered in a junior course, they are approached much more rigorously here. The proofs of theorems are often brief and lack in detail. While there are exercises provided at the end of each section, there are no solutions or hints provided anywhere in the text, nor is there a solution manual available for purchase. Many undergraduates will find this quite frustrating and may have to resort to purchasing a supplementary text which includes problems with solutions. While this book is efficient and moderately priced, the content and presentation is less than sufficient for most undergraduates.
O'Neill, B. Elementary Differential Geometry-2nd edition. Academic Press, San Diego, CA, 1997.
Reviewed by Dan Wolczuk, wolczu0@unbc.ca.
To be to the point, I am not very impressed by this text book. The two main problems I have with this book are that some definitions and formulas are hidden amongst regular text, and that there is a major lack of descriptive examples. If it were not for the former problem I would believe that this would make a good reference book, but unfortunately you cannot find all of the necessary definitions and theorems by merely scanning the pages. The lack of examples makes the textbook fairly difficult to learn from as the explanations of concepts and proofs of theorems are not always complete. The questions at the end of each chapter are the only part of the book I have to commend. They do an excellent job of ensuring an understanding of the material from the previous chapters. For example, in doing questions from Chapter 4, if you do not have a good grasp of the previous three chapters you will find the questions quite difficult. However, with a good understanding of the necessary material many of the questions are quite trivial. Overall I am not at all a fan of this book, although I have definitely learned the necessary material from it, so it cannot be all that bad.
Ross, Kenneth A. Elementary Analysis: The Theory of Calculus. Springer-Verlag, 1980.
Reviewed by Raymond Cheng, kwrcheng@ucalgary.ca.
The book is rigorously written and is extremely good for math majors. I don't think this book is very suitable for non-math majors however, since they might think it's too dull. The book does not go on and on like some math textbooks with non-essential talk. It gets into the material right away. The proofs have been carefully chosen so that they're as simple and as elegant as possible. Topology is treated in optional sections, and the focus of the book is sequences. Indeed, the treatment of sequences is very thorough. Also, many notions are also defined in terms of sequences. However, proof that this definition and the usual delta-epsilon definition are equivalent is given. The style of writing is clear, concise, and avoids unnecessary discussion. Proofs are given out in full and are seldom left to the readers as an exercise. In keeping with the style of this book, historical facts and references are not provided. I think this book should be a must-have for all math undergrads. Pi in the Sky. The Pacific Institute for the Mathematical Sciences, June 2000. Available at (opens in new window): http://www.pims.math.ca/pi
Reviewed by Raymond Cheng, kwrcheng@ucalgary.ca.
Pi in the Sky is a semiannual mathematical magazine targeted at junior and senior high school students and educators. However, I find that some of the content might be too advanced and the magazine as a whole might be more appropriate for undergraduates. There are nearly ten articles in this periodic publication along with jokes, comics and other interesting materials. As stated in the publication, ``This journal is devoted to cultivating mathematical reasoning and problem-solving skills, to prepare students for the challenges of the high-technology era." The magazine is professionally produced and if you plan to read it from cover to cover, it will set you back a couple of hours. There are some interesting math questions at the end of the magazine, and the reader is invited to submit solutions. Overall, I think this journal is a good read for all math undergraduate students as well as advanced high school students.
In Your Area
UNBC website
Dan Wolczuk at the University of Northern British Columbia (UNBC) was the first to reply to our e-mail and the first to complete a website. His website can be reached via our website http://www.cms.math.ca/Students by following the links in your area, mathematics at UNBC. Great job Dan!UCAL website
Raymond Cheng at the University of Calgary (UCAL) has also completed a website. His website can be reached via our website by following the links in your area, Calgary. Great job Raymond!UBC website
In process. Adrien Desjardins at the University of British Columbia (UBC) is the webmaster.Calender
Here we intend to list mathematical events and deadlines throughout the year which appear on our website http://www.cms.math.ca/Students under Calender.If you have an event or deadline which you would like to include, visit our website and drop our webmaster Andrew Irwin a line. Andrew J. Irwin 2001-03-19
