Resources
The purpose of this page is to provide students with interesting resources for learning about mathematics. If you have a favorite site that you think would fit in here, please email Mr. MacLennan.
Caution: these sites are interesting! Note that viewing these sites is no substitute for actually doing (and learning by doing) mathematics. In other words, first complete your practice assignment to the best of your ability, then explore one of these sites.
Mr. MacLennan has one, most-important overall measure of how your mathematical day went: How many problems did you solve?
Caution: these sites are interesting! Note that viewing these sites is no substitute for actually doing (and learning by doing) mathematics. In other words, first complete your practice assignment to the best of your ability, then explore one of these sites.
Mr. MacLennan has one, most-important overall measure of how your mathematical day went: How many problems did you solve?
Mathematics
The Elements of Math
In 2010, Cornell Mathematics Professor Steven Strogatz wrote 15 columns in the New York Times about various mathematics topics, from why numbers are useful to the intricacies of infinity. Mr. MacLennan has even borrowed one of his arguments to promote Math Team.
Explained Visually
As its name implies, this site attempts to explain mathematical topics visually, via clever animations. High-school mathematics topics (pi, exponentiation, sine and cosine) are here, as are several post-secondary mathematics topics.
Khan Academy
Thousands of mostly short (< 10 minutes) informal videos, many on mathematics topics. Excellent for both new learning and review. Earning points and badges adds to the fun.
The Math Dude
Jason Marshall is an astrophysicist who explains math concepts very well in this podcast that gives you "quick-and-dirty tips to make math easier." Each episode is about 8 minutes. It unfortunately includes a commercial to pay the bills, but ignore that and you've got some memorably interesting math tips.
Numberphile
YouTube channel with many math-related videos,often consisting of annotated interviews with practicing mathematicians.
PBS Infinite Series
Thirty (and counting) short (7-17 minutes) videos on various mathematical topics, often touching on some highly advanced (and thus highly mind-blowing) topics. Developed by PBS Digital Studios, which produces other interesting series such as Crash Course Astronomy, It's Okay to Be Smart, Physics Girl, and ViHart).
Wolfram MathWorld
Rigorous mathematics definitions and explanations, with listed sources for further explanation. Developed and maintained by Eric Weisstein, a contributor to Stephen Wolfram's development of the powerful Mathematica and Wolfram Alpha applications.
In 2010, Cornell Mathematics Professor Steven Strogatz wrote 15 columns in the New York Times about various mathematics topics, from why numbers are useful to the intricacies of infinity. Mr. MacLennan has even borrowed one of his arguments to promote Math Team.
Explained Visually
As its name implies, this site attempts to explain mathematical topics visually, via clever animations. High-school mathematics topics (pi, exponentiation, sine and cosine) are here, as are several post-secondary mathematics topics.
Khan Academy
Thousands of mostly short (< 10 minutes) informal videos, many on mathematics topics. Excellent for both new learning and review. Earning points and badges adds to the fun.
The Math Dude
Jason Marshall is an astrophysicist who explains math concepts very well in this podcast that gives you "quick-and-dirty tips to make math easier." Each episode is about 8 minutes. It unfortunately includes a commercial to pay the bills, but ignore that and you've got some memorably interesting math tips.
Numberphile
YouTube channel with many math-related videos,often consisting of annotated interviews with practicing mathematicians.
PBS Infinite Series
Thirty (and counting) short (7-17 minutes) videos on various mathematical topics, often touching on some highly advanced (and thus highly mind-blowing) topics. Developed by PBS Digital Studios, which produces other interesting series such as Crash Course Astronomy, It's Okay to Be Smart, Physics Girl, and ViHart).
Wolfram MathWorld
Rigorous mathematics definitions and explanations, with listed sources for further explanation. Developed and maintained by Eric Weisstein, a contributor to Stephen Wolfram's development of the powerful Mathematica and Wolfram Alpha applications.
Applied Mathematics
A leading Silicon Valley engineer explains why every tech worker needs a humanities education Software developer Tracy Chou, who has worked at Quora and Pinterest, writes how an excellent liberal arts education leads to writing excellent code.
College Applications
How to write a good college application essay
An essay should explain why a student wishes to attend a particular college and not others.
An essay should explain why a student wishes to attend a particular college and not others.
Competitive Mathematics
The following resources support student participation in mathematics competitions. Please contact Mr. MacLennan if you are interested in participating in any listed activity.
American Mathematics Competition 8 (AMC 8)
The AMC 8 is for students in grade 8 and below. The exam is typically given in November.
American Mathematics Competition 10/12 (AMC 10/12)
The AMC 10 is for students in grades 10 and below. The AMC 12 is for students in grades 11 and 12. The exams are typically given twice, about a week apart, in late January and/or early February.
Art of Problem Solving (AoPS)
The premier website for competitive mathematics preparation. AoPS offers books, videos, and forums.
Minnesota MATHCOUNTS and MATHCOUNTS
MATHCOUNTS competitions are for students in grades 6 to 8. The Minnesota MATHCOUNTS regional exam follows the MJHML season in February. Individuals and teams may advance to the Minnesota MATHCOUNTS state competition in March and the MATHCOUNTS national competition in May.
Minnesota Junior High Math League (MJHML)
MJHML is for students in grades 6 to 8. The season consists of 5 meets,held from September through January. MJHML is the best preparation for MSHSML.
Minnesota State High School Mathematics League (MSHSML)
MSHSML is for students in grades 9 to 12. Students in lower grades may participate if they have (1) completed Algebra 1, (2) have completed or are currently enrolled in either Geometry or Algebra 2 (or both), and (3) have sufficiently demonstrated (as determined by coaches) sufficient ability.
American Mathematics Competition 8 (AMC 8)
The AMC 8 is for students in grade 8 and below. The exam is typically given in November.
American Mathematics Competition 10/12 (AMC 10/12)
The AMC 10 is for students in grades 10 and below. The AMC 12 is for students in grades 11 and 12. The exams are typically given twice, about a week apart, in late January and/or early February.
Art of Problem Solving (AoPS)
The premier website for competitive mathematics preparation. AoPS offers books, videos, and forums.
Minnesota MATHCOUNTS and MATHCOUNTS
MATHCOUNTS competitions are for students in grades 6 to 8. The Minnesota MATHCOUNTS regional exam follows the MJHML season in February. Individuals and teams may advance to the Minnesota MATHCOUNTS state competition in March and the MATHCOUNTS national competition in May.
Minnesota Junior High Math League (MJHML)
MJHML is for students in grades 6 to 8. The season consists of 5 meets,held from September through January. MJHML is the best preparation for MSHSML.
Minnesota State High School Mathematics League (MSHSML)
MSHSML is for students in grades 9 to 12. Students in lower grades may participate if they have (1) completed Algebra 1, (2) have completed or are currently enrolled in either Geometry or Algebra 2 (or both), and (3) have sufficiently demonstrated (as determined by coaches) sufficient ability.
Edible Mathematics
Lessons of the Mobius bagel An interesting "twist" on the Mobius strip via slicing of a bagel (a torus to us mathematicians) and a brief reflection on the uncanny tendency for seemingly speculative mathematics to sprout practical applications centuries later.
History of Mathematics
A Brief History of Mathematics
Professor Marcus du Sautoy's exploration of the human drama in mathematics in ten deliciously digestible 15-minute podcasts.
Babylon and on and on....
Did the Babylonians create the first trigonometric table? Researchers at the University of New South Wales think so.
On This Day
Mathematics history by day, from the Mathematical Association of America. Find out what mathy things happened on your birthday!
Professor Marcus du Sautoy's exploration of the human drama in mathematics in ten deliciously digestible 15-minute podcasts.
Babylon and on and on....
Did the Babylonians create the first trigonometric table? Researchers at the University of New South Wales think so.
On This Day
Mathematics history by day, from the Mathematical Association of America. Find out what mathy things happened on your birthday!
Modern Mathematicians
Let us define a "modern" mathematician as one who is or was active in mathematics during this, the twenty-first century. There are of course many (thousands), but here are just a few about whom general-publication articles have been written::
Vi Hart
Vi Hart
- Home page Vi Hart is a sassy young mathematician who doesn't like pi. (She prefers tau instead--as does Mr. MacLennan!)
- YouTube channel Vi made her name with her smart videos. Viewing these does not give you permission to doodle in class.
- Maryam Mirzakhani, only woman to win a Fields Medal, dies at 40 Dr. Mirzakhani was born in Iran and taught at Stanford University. She was awarded the Fields Medal in 2014.
- With snowflakes and unicorns, Marina Ratner and Maryam Mirzakhani explored a universe in motion Interesting article on the work of two highly acclaimed female mathematicians who recently passed.
- Home page Dr. Tao's site emphasizes his current research, but his status as a former child prodigy means his career advice for students of all ages is worth a look.
- The singular mind of Terence Tao Considered by some the greatest living mathematician. Dr. Tao, from Australia, is a mathematics professor at UCLA.
Numbers
How a church deacon found the biggest prime number yet (it wasn't as hard as you think) The 50th Mersenne prime was announced 3 January 2018.
New biggest prime number = 2 to the 74 mil... uh, it's big The 49th Mersenne prime was found in January 2016.
New biggest prime number = 2 to the 74 mil... uh, it's big The 49th Mersenne prime was found in January 2016.
Practical Mathematics
The geometry of perfect parking How can one use properties of circles and the Pythagorean Theorem to parallel park?
How to make a big decision. Have no fear. An emerging science can now help you choose.
How to pick the fastest line at the supermarket This article (with funny video) looks at the math behind waiting in line.
The math of social distancing is a lesson in geometry Maintaining a six-foot distance is like the classic "sphere packing" problem.
How to make a big decision. Have no fear. An emerging science can now help you choose.
How to pick the fastest line at the supermarket This article (with funny video) looks at the math behind waiting in line.
The math of social distancing is a lesson in geometry Maintaining a six-foot distance is like the classic "sphere packing" problem.
Recreational Mathematics
Children of the cube Notes from the CubingUSA Nationals, where Rubik's Cube and a dizzying array of variants hold sway.
The importance of recreational mathematics Math for fun, in the spirit of the great Martin Gardner.
Studying (in General)
College advice I wish I'd taken A teacher looks back with regret on being the type of mediocre student she now disdains. (10/17/2017)
How to get your mind to read Comprehension begins with what you know. Let's start there.
Why fidgeting is good medicine Sitting all day? Fidgeting your legs may be good for your health.
How to get your mind to read Comprehension begins with what you know. Let's start there.
Why fidgeting is good medicine Sitting all day? Fidgeting your legs may be good for your health.
Studying Mathematics
Algorithmic education (including the mathematics of cramming) Should you study new material or review? How long? And how often? Some mathematicians examine these questions.
How to learn math (for students) Short (4:24) YouCubed video about having a growth mindset. (10/14/2017)
Survey: Habits of talented mathematics students What do talented mathematics students study? Or perhaps we should instead ask, what habits result in talented mathematics students?
How to learn math (for students) Short (4:24) YouCubed video about having a growth mindset. (10/14/2017)
Survey: Habits of talented mathematics students What do talented mathematics students study? Or perhaps we should instead ask, what habits result in talented mathematics students?
Summer Mathematics (and Science) Programs
Math League Summer Institute A one-week residency program at Augsburg University in Minneapolis, sponsored by the Minnesota State High School Mathematics League, for current (prior to summer) 6th- to 11th-grade students.
Scientific Discovery Program A month-long residency science program at St. Cloud University for current (prior to summer) 9th- and 10th-grade students.
Scientific Discovery Program A month-long residency science program at St. Cloud University for current (prior to summer) 9th- and 10th-grade students.
Taking Notes
Laptops are great. But not during a lecture or a meeting. What happens when you use a laptop to take notes? You learn less--and so does everyone around you.
Taking Tests
How I learned to take the SAT like a rich kid Want to do well on the Scholastic Aptitude Test (SAT)? Read this for some potentially helpful hints.
A surprisingly simple way to help level the playing field of college admissions Short answer: take the SAT early and often. It's what kids from wealthy families do, and there are supports for non-wealthy families.