I have some time to think about things, and I got hung up on a detail…and the resolution of said detail was realizing, that if is a bijection (one to one and onto), then .

ARRRGGGHHHHH!!!!!!!!!!!!

Back to work.

Advertisements

I have some time to think about things, and I got hung up on a detail…and the resolution of said detail was realizing, that if is a bijection (one to one and onto), then .

ARRRGGGHHHHH!!!!!!!!!!!!

Back to work.

Advertisements

RSS feed for comments on this post. TrackBack URI

## Categories

- academia (54)
- advanced mathematics (109)
- algebra (8)
- algebraic curves (7)
- analysis (37)
- anova (1)
- applications of calculus (14)
- applied mathematics (61)
- basic algebra (17)
- books (4)
- calculus (124)
- calculus of variations (2)
- cantor set (2)
- cantor space (1)
- change of variable (1)
- class room experiment (14)
- complex variables (12)
- conference (7)
- data fitting (4)
- density function (3)
- derivatives (14)
- differential equations (31)
- dirac delta function (1)
- distributions (3)
- economics (4)
- editorial (78)
- elementary mathematics (28)
- elementary number theory (6)
- elliptic curves (2)
- evolution (2)
- famous mathematicians (3)
- Fourier Series (7)
- generalized functions (3)
- geometry (2)
- grade inflation (1)
- how to learn calculus (4)
- hypothesis testing (2)
- implicit differentiation (1)
- improper integrals (4)
- Impulse (1)
- induction (3)
- infinite series (4)
- infinity (2)
- inflection points (1)
- integrable function (6)
- integrals (37)
- integration by substitution (9)
- knot theory (3)
- Laplace transform (8)
- Lebesgue Integration (9)
- likelihood function (1)
- linear albegra (16)
- linear regression (2)
- logic (4)
- mathematical ability (13)
- mathematical economics (2)
- mathematician (6)
- mathematics education (41)
- matrix algebra (5)
- Measure Theory (8)
- media (32)
- movies (1)
- negative binomial distribution (1)
- news (12)
- non elementary integrals (3)
- Normal distribution (2)
- number theory (9)
- numerical methods (17)
- numerical solution of differential equations (5)
- optimization (7)
- partial differential equations (6)
- pedagogy (54)
- physics (24)
- point set topology (9)
- popular mathematics (21)
- Power Series (4)
- probability (25)
- quantum mechanics (20)
- recreational mathematics (5)
- research (21)
- ring theory (1)
- science (29)
- sequences (13)
- sequences of functions (5)
- series (14)
- statistics (23)
- student learning (30)
- sufficient statistics (1)
- Taylor Series (4)
- topology (34)
- transfinite induction (2)
- Uncategorized (9)
- uniform convergence (3)
- uniqueness of solution (5)
- vector calculus (3)
- vector spaces (3)
- well posed problem (1)

## Blogroll

- Alberto Delgado's Calculus Page Math Professors teaching blog
- Bradley University Mathematics Department math department webpage
- Cameron Gordon Knot Theorist’s web page
- Cosmic Variance Cosmology but contians some nice math articles from time to time
- Electoral Vote Political Statistics
- Five Thirty Eight (Nate Silver and others) Political Statistics
- Good Math, Bad Math General Mathematics
- Interactive Differential Equations Tools for visualizing solutions to several common differential equations
- John Polking Mathematician web page
- Jon Simon Knot Theorist’s web page
- Louis Kauffman Knot Theorist’s web page
- Low Dimensional Topology Mathematics blog (specialized)
- Matlab Software for Numerical Methods and Analysis MATLAB software packages for numerical methods
- Morwen Thistlethwaite Knot Theorist’s web page
- NIST Digital Library of Mathematical Functions Lots of functions here.
- Ordinary Differential Equations with MATLAB ODE software for MATLAB
- Overdetermined Political Statistics
- Recursivity (Jeffrey Shallit ) Personal Blog (mathematician)
- Statistical Modeling, Causal Inference, and Social Science Applied Statistics
- Steven Strogatz, New York times Popular Mathematics (for the non-mathematician)
- Terry Tao's blog Personal Blog (mathematician)
- Topology Atlas topology preprints, conference announcements, etc.
- Unapologetic Mathematician Personal Blog (mathematician)
- University of Illinois Urbana-Champaign Math Department webpage
- Wolfram Math World Mathematical Reference

## Archives

- December 2016 (1)
- November 2016 (2)
- October 2016 (5)
- September 2016 (1)
- August 2016 (2)
- June 2016 (3)
- May 2016 (1)
- April 2016 (1)
- February 2016 (5)
- January 2016 (6)
- December 2015 (2)
- October 2015 (2)
- September 2015 (2)
- August 2015 (2)
- July 2015 (4)
- June 2015 (3)
- May 2015 (4)
- April 2015 (4)
- March 2015 (9)
- February 2015 (5)
- January 2015 (11)
- December 2014 (2)
- November 2014 (5)
- October 2014 (7)
- September 2014 (6)
- August 2014 (15)
- July 2014 (6)
- May 2014 (2)
- April 2014 (5)
- March 2014 (13)
- February 2014 (8)
- January 2014 (5)
- December 2013 (6)
- November 2013 (9)
- October 2013 (9)
- September 2013 (9)
- August 2013 (1)
- July 2013 (5)
- June 2013 (3)
- May 2013 (6)
- April 2013 (7)
- March 2013 (6)
- February 2013 (9)
- January 2013 (3)
- December 2012 (5)
- November 2012 (1)
- October 2012 (1)
- September 2012 (4)
- August 2012 (5)
- July 2012 (1)
- June 2012 (2)
- May 2012 (5)
- April 2012 (3)
- March 2012 (3)
- February 2012 (4)
- January 2012 (2)
- December 2011 (1)
- November 2011 (1)
- October 2011 (2)
- September 2011 (2)
- August 2011 (13)
- July 2011 (7)
- May 2011 (4)
- April 2011 (3)
- March 2011 (3)
- February 2011 (3)
- January 2011 (9)
- October 2010 (1)
- September 2010 (5)
- May 2010 (1)
- April 2010 (3)
- March 2010 (11)

## Top Clicks

## Top Posts

- Why Some Students Can't Learn Elementary Calculus: a conjecture
- Lebesgue Measure: Outer Measure, Measure, Why the Caratheodory Criterion works
- Pointwise vs. Uniform convergence for functions: Importance of being continuous
- Why the sequence cos(n) diverges
- Finding a Particular solution: the Convolution Method
- A Laplace Transform of a function of non-exponential order
- Stupid question: why does it appear to us that differentiation is easier than anti-differentiation?
- The Principle of Mathematical Induction: why it works
- Radial plane: interesting topology for the plane
- The Dirac Delta Function in an Elementary Differential Equations Course

%d bloggers like this:

[…] I worked on some…and was anguished at the elementary mistakes I made. Now if you want to see some of what world class mathematicians work on, read this. This is a […]

Pingback by Math, abs and bench presses « blueollie — April 10, 2015 @ 1:01 am