WHATMaths

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[whatmaths-blog]

Binomial Coefficients

Level: A-level Mathematics and above 

About: 

A binomial coefficient nCk, also known as a combination or combinatorial number, is the number of unordered ways to choose k items from a set of n items, where n and k are non-negative integers. As the name suggests, they are coefficients in the binomial theorem.

Ever wondered where the entries for Pascal's triangle come from?         They're binomial coefficients! In this case, n is the row number,and k is the 'column' number. Both n and k start at 0, and k goes up to n in each row.

Our lesson below goes through finding binomial coefficients using your calculator and how to form Pascal’s triangle, and we have some worksheets for you to get the hang of everything. So check them out!

Lesson resources:

Presentation

Task sheets: 1, 2, 3

[actuallyvady]

A limerick:

Doesn’t look like a limerick to you? Try this:

A dozen, a gross, and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit more.

[whatmaths-blog]

Algebraic Division

Level: GCSEs and above (this is an introduction into the techniques of dividing algebraic expressions)

About:

Algebraic Division is the process of dividing one polynomial by another. 

It is the generalised version of the arithmetic technique of long division, which you will have learnt earlier, and it is a useful tool as it allows you break down complex algebraic problems into more simple expressions. 

For a step-by-step guide of how to do this, with some helpful hints and key definitions, check out our lesson and exercises below!

Lesson resources:

Presentation

Task sheets: 1, 2, 3

[sixpenceee]

Margaret Hamilton is a computer scientist and mathematician. She was the lead software engineer for Project Apollo.  Her work prevented an abort of the Apollo 11 moon landing. She’s also credited for coining the term “software engineer.” 

[nowonlyghosts]

Those stacks are the code she wrote for Apollo 11. Incredible.

[phryne-fish]

reblog all the time

[the-movemnt-deactivated20170912]

Hidden Figures Upholds the Legacy of 3 Extraordinary Black Women Who Changed the World

Hidden Figures is the riveting and inspirational story of three black female mathematicians who excelled against all odds at NASA. Many of us are just now learning their names: Katherine Johnson, Mary Jackson and Dorothy Vaughn.

[celebratingamazingwomen]

Charlotte Scott (1858-1931) was a British mathematician who spent much of her life and career in the United States, where she had a considerable influence on the development of the field of mathematics in general and the education of women in particular. She was educated at the University of Cambridge, and in 1885 became the first British woman to receive a doctorate.

She obtained special permission to take the Cambridge Mathematical Tripos exam, as females were not usually allowed; even though she came eighth, the prize went to a male student with a lower grade. After the incident, however, public pressure led to her accomplishment being celebrated and women being formally allowed to take the exam thereafter. In 1891 she became the first woman in the New York Mathematical Society, and supervised the PhD theses of many early female mathematicians.

[profeminist]

Today’s Google Doodle is STEM goddess (engineer / mathematician / physicist / inventor) Hertha Ayton!

http://www.google.com/doodles/hertha-marks-ayrtons-162nd-birthday

“Phoebe Sarah Hertha Ayrton (28 April 1854 – 23 August 1923), was a British engineer,mathematician, physicist, and inventor. Known in adult life as Hertha Ayrton, née Phoebe Sarah Marks, she was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripples in sand and water.

Ayrton helped found the International Federation of University Women in 1919 and the National Union of Scientific Workers in 1920.”

Source

[redeemeve]

This is a great honor. I will be happy if it encourages young female scientists and mathematicians. I am sure there will be many more women winning this kind of award in coming years…

Dr. Maryam Mirzakhani on being the first woman to win a Fields Medal, the mathematics’ equivalent of the Nobel Prize. (via redeemeve)

[halfsyproblems]

Rroma You Should Know: Sofia Kovalevskaya

Born to a Polish father and a Rromani mother in Moscow in 1850, Kovalesvskya was the first prominent female mathematician in Russian history, as well as one of the first women to serve as an editor on a major scientific journal. She was the first woman in Europe to earn a doctorate degree summa cum laude, and her many mathematical and scientific accomplishments (and much lobbying on her part to change the Academy’s sexist membership rules) eventually earned her a spot in the Russian Academy of Sciences. Though she sadly died at the young age of 41, she accomplished a great deal in her few years, including the Cauchy-Kowalevski Theorem and the Kovalevskaya Top.

[olennaredwyne]

Badass History Ladies - Hypatia of Alexandria

“Reserve your right to think, for even to think wrongly is better than not to think at all.”

Said to have been the last librarian of the Library of Alexandria, Hypatia is the first recorded female mathematician. She edited works of science and math, and invented the hydrometer (a device which helps measure the gravity and density of liquids).

There are two accounts of her death. The first, and most widely accepted, was written soon after her dead in 415 CE. According to the historian, Hypatia was murdered by a Christian mob for her political influence and heresy.

[celebratingamazingwomen]

Mary Cartwright (1900-1998) was a British mathematician who was the first to analyse a dynamical system with chaos. She was the first woman to obtain a first-class degree in Mathematics from the University of Oxford.

She also obtained her PhD in Oxford, and went on to work as a researcher in Cambridge. In 1930 she began work on the theorem that now bear her name (Cartwright’s theorem). She was elected as a Fellow of the Royal Society in 1947, the first female mathematician to be offered this honour.

[ibmblr]

Meet the real women behind Hidden Figures.

In the early days of the Space Race, Dorothy Vaughan headed the National Advisory Committee for Aeronautics’ (NACA) West Area Computing unit. It was an important but segregated unit of mostly female mathematicians doing aerospace calculations by hand. When NACA became NASA in 1958, the Analysis and Computation Division desegregated and Vaughan became a sought-after expert on FORTRAN  – a programming language used on IBM mainframes.

Vaughan is one of the women whose work inspired the film Hidden Figures — a true story of three African American mathematicians who helped NASA launch the first Americans into space.

Feeling inspired? See how coding might figure into your life. Uncover more about Dorothy Vaughan →

[cuppa-studies]

[science]

[maxwellsequations]

Each trig function in terms of the other five: color coded. Idk I’m just playin’ around in LaTeX and thought this table on Wikipedia would be worth color coding on its own so I made this little ditty. The reciprocal functions are the lighter colors of their regular trig counterparts. I wouldn’t call this a final version, but, hey, it’s pretty cute. High five for pattern recognition.

[organizeandstudy]

Reblog to save a life

[hurricane-euler]

*nervous laughter*

[whatmaths-blog]

Complex Numbers

Level: GCSEs and above (this is only an introduction to imaginary and complex numbers, and sticks to the basic operations of addition, subtraction, multiplication, and division that does not involve complex conjugates, i.e. dividends with a real factor)

About:

A complex number is a number which can be expressed in real and imaginary parts, which looks like a + bi, where a and b are both real numbers, and i is the imaginary unit such that i2 = -1. Here, a is the real part and bi is the imaginary part. 

Adding, subtracting, multiplying and dividing with complex numbers works similar to the same operations on algebraic expressions except instead of an unknown variable x or y, we work with i. 

Try our lesson and examples below and you'll get the hang of it!

Lesson resources:

Presentation

Task Sheets: 1, 2, 3