Prime numbers | Mathematical fallacies | Theorems in ring theory | Algebra education
The freshman's dream is a name sometimes given to the erroneous equation , where is a real number (usually a positive integer greater than 1) and are nonzero real numbers. Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums. When n = 2, it is easy to see why this is incorrect: (x + y)2 can be correctly computed as x2 + 2xy + y2 using distributivity (commonly known by students as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem. The name "freshman's dream" also sometimes refers to the theorem that says that for a prime number p, if x and y are members of a commutative ring of characteristic p, then (x + y)p = xp + yp. In this more exotic type of arithmetic, the "mistake" actually gives the correct result, since p divides all the binomial coefficients apart from the first and the last, making all intermediate terms equal to zero. The identity is also actually true in the context of tropical geometry, where multiplication is replaced with addition, and addition is replaced with minimum. (Wikipedia).
A mistake that is not wrong | Shorts #3
Freshman's dream is famous for being utterly wrong. But is it? Even though many people made this mistake when they first learned algebra, is it possible that it is in some sense right? Useful link: https://en.wikipedia.org/wiki/Freshman%27s_dream Other than commenting on the video, you ar
From playlist Novel topics (not in usual math curricula)
The Class of 2014 on graduating
In the weeks leading up to Commencement Weekend, Stanford seniors shared their feelings on graduating. #Stanford14
From playlist #Stanford14 Commencement
Debra Satz - Dean, School of Humanities & Sciences
Stanford Celebration of 2020 Graduates
From playlist Stanford Class of 2020 Virtual Celebration
From playlist Life at ASU
What is a Successful Semester in College? Did You Have One?
In this video I talk about what exactly is a "successful semester" in college. I give one example from my personal experience. Do you think your semester was successful? Why or why not? If you enjoyed this video please consider subscribing for more content: https://www.youtube.com/user/th
From playlist Cool Math Stuff
During New Student Orientation, incoming freshmen and transfer students dive into the academic, social and cultural life of Stanford. ___________ Special thanks to Harry Elam, Deborah Golder, Michael Tubbs, '12, MA '12, Kate Mayer, Christopher Vassos and Dustin Fink.
From playlist New Student Orientation 2013
Video Yearbook: #ASUgrad Class of 2017 | Arizona State University
Class of 2017: This is you. Check out our video yearbook highlighting some of the most memorable moments from the last 4 years. Congratulations ASU grads!
From playlist Graduation at ASU
Things such as finances, relationships, increased responsibility, stress and mental disorders are all things teens can experience in life. Transitions, the first of its kind resource, provides readers with self-help information in which they can not only use for themselves, but with friend
From playlist Transitions
The Freshman's Dream, Explained: If a+b=c, a² + b² = c² too?
The Freshman's Dream: the mistake so common, they gave it its own Wikipedia page. Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications 🔔 When students begin to multiply binomials or solve for the lengths of right triangles, inevitably this question comes up: shouldn't
From playlist Math Mini
Stanford welcomes Class of 2020
Students, staff and President Marc Tessier-Lavigne greet incoming freshman from the Class of 2020 as they move into their residence halls.
From playlist Stanford Highlights
Purpose and Change Coach | Navigating career change | Part 4 | Khan Academy
A professional coach talks about why he left a job in finance after realizing that his "dream career" wasn't right for him. Learn how Alex navigated the challenges of career change and ultimately started his own business, Frable Consulting. This video is part of a series on Khan Academ
From playlist Career Profiles
The Sexual Fantasies of Others
Despite talk of liberation, our sexual lives remain the focus of immense amounts of shame. One way to deal with this is to expand - with dignity - evidence of what people are truly like. Here, some brave individuals reveal what it is they deep down want and think about. We applaud their co
From playlist RELATIONSHIPS
Teaching Freshman Math & Science to the Masses
(February 10, 2011) Ralph Cohen shares how math and science can best be taught to the masses. He focuses on the programs that deliver math and science to Stanford freshman, as well as some of Stanford's service classes. The Center for Teaching and Learning's longest-running lecture series
From playlist Feature | Center for Teaching and Learning
Trace Guzmán '21: Setting the stage
Trace Guzmán, who grew up in Texas, will graduate with a bachelor’s degree in management science and entertainment, and plans to move to Los Angeles to pursue a career in acting. MB01CE1FL6MAUBO
From playlist Stanford Class of 2021
What Matters To Me and Why: Erin Gruwell and Julia Reinhard Lupton
Recorded on January 12, 2016.
From playlist What Matters to Me and Why
Hear about the college experience from current students. Then, go to https://www.khanacademy.org/college-admissions for Khan Academy's complete college admissions and financial aid resource!
From playlist Getting started | College Admissions | Khan Academy
Stanford Welcomes Class of 2016
September 18, 2012 - Students, staff and President Hennessy greet incoming freshman from the Class of 2016 as they move into their residence halls. Stanford University: http://www.stanford.edu/ Stanford News: http://news.stanford.edu/ Stanford University Channel on YouTube: http://www.y
From playlist Stanford News 2012