Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts
Tuesday, May 3, 2016
Thursday, March 31, 2016
Thursday, April 30, 2015
Check out MathWorld
"MathWorld TM
is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica.
MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors. Since its contents first appeared online in 1995, MathWorld has emerged as a nexus of mathematical information in both the mathematics and educational communities. It not only reaches millions of readers from all continents of the globe, but also serves as a clearinghouse for new mathematical discoveries that are routinely contributed by researchers. Its entries are extensively referenced in journals and books spanning all educational levels, including those read by researchers, elementary school students and teachers, engineers, and hobbyists"
Check out MathWorld
is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica.
MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors. Since its contents first appeared online in 1995, MathWorld has emerged as a nexus of mathematical information in both the mathematics and educational communities. It not only reaches millions of readers from all continents of the globe, but also serves as a clearinghouse for new mathematical discoveries that are routinely contributed by researchers. Its entries are extensively referenced in journals and books spanning all educational levels, including those read by researchers, elementary school students and teachers, engineers, and hobbyists"
Check out MathWorld
Kurt Gödel's Incompleteness Theorems meanings
Who was Kurt Godel
"Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions … It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced."
See numerous explanations @ Miskatonic University Press
Gödel’s Incompleteness Theorem says:
“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”
Stated in Formal Language:
Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”
"Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions … It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced."
See numerous explanations @ Miskatonic University Press
Gödel’s Incompleteness Theorem says:
“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”
Stated in Formal Language:
Gödel’s theorem says: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”
Who was Kurt Godel?
"Kurt Friedrich Gödel was born on April 28,1906, in what was at that time Brünn, a city in the Austrian-Hungarian Monarchy, today's Brno in Czech Republic. He was the son of Rudolf Gödel and Marianne Handschuh and had one elder brother, Rudolf. His father was the owner of a textile firm in Brünn. After attending school in Brünn and graduating with honors, Kurt enrolled at the University of Vienna in 1923, where he completed his doctoral dissertation under Hans Hahn in 1929. In 1930 he became a member of the same university, which he would remain until 1938, the year that Austria became part of nazi Germany (the Anschluß).
During his life Gödel received several prizes and honourable memberships (and rejected some others). Among the prizes he received are the Einstein Award (1951) and the National Medal of Science (1974). He was a member of the National Academy of Sciences of the United States, a fellow of the Royal Society, a member of the Institute of France, a fellow of the Royal Academy and an Honorary Member of the London Mathematical Society."
See entire biography @ The Kurt Godel Society
"Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.
During his life Gödel received several prizes and honourable memberships (and rejected some others). Among the prizes he received are the Einstein Award (1951) and the National Medal of Science (1974). He was a member of the National Academy of Sciences of the United States, a fellow of the Royal Society, a member of the Institute of France, a fellow of the Royal Academy and an Honorary Member of the London Mathematical Society."
See entire biography @ The Kurt Godel Society
"Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.
Thursday, April 2, 2015
Thursday, March 5, 2015
Pay attention when tracking calories!!! by WLI
Let's use a Bolthouse Farms drink as an example (I am currently drinking one and I just now discovered this) Now, if I tractl 16 oz, or 2 servings of 8 oz, that brings my caloric intake to 240. But, 15.2 oz = 247 calories.
1) I am allowed more calories than I have been tracking=more yummy food
2) I am putting my body into negative calorie mode and my body is not getting the calories it needs to function..
3) It may prevent weight loss goals.
So, to find out the correct number you may need to do some math,or just make your you track the correct amount of oz and the correct amount of servings.Just use division between the total amount of calories and how many oz (I think, that's what I have been doing, if I am wrong let me know)
1) I am allowed more calories than I have been tracking=more yummy food
2) I am putting my body into negative calorie mode and my body is not getting the calories it needs to function..
3) It may prevent weight loss goals.
So, to find out the correct number you may need to do some math,or just make your you track the correct amount of oz and the correct amount of servings.Just use division between the total amount of calories and how many oz (I think, that's what I have been doing, if I am wrong let me know)
Thursday, January 8, 2015
Monday, December 29, 2014
Who was Al-Jazari?
"Badi'al-Zaman Abū al-'Izz ibn Ismā'īl ibn al-Razāz al-Jazarī (1136–1206) (Arabic: بديع الزمان أَبُو اَلْعِزِ بْنُ إسْماعِيلِ بْنُ الرِّزاز الجزري) was a Muslim polymath: a scholar, inventor, mechanical engineer, craftsman, artist, and mathematician from Jazirat ibn Umar (current Cizre, Turkey), who lived during the Islamic Golden Age (Middle Ages).
He is best known for writing the al-Jāmiʿ bain al-ʿilm wa al-ʿamal al-nāfiʿ fī ṣināʿat al-ḥiyal (The Book of Knowledge of Ingenious Mechanical Devices) in 1206, where he described 100 mechanical devices, some 80 of which are trick vessels of various kinds, along with instructions on how to construct them"
See more@ Wikipedia
More Info..
He is best known for writing the al-Jāmiʿ bain al-ʿilm wa al-ʿamal al-nāfiʿ fī ṣināʿat al-ḥiyal (The Book of Knowledge of Ingenious Mechanical Devices) in 1206, where he described 100 mechanical devices, some 80 of which are trick vessels of various kinds, along with instructions on how to construct them"
See more@ Wikipedia
More Info..
Tuesday, December 23, 2014
[Pic:] Weight, calories, fat scientifically defined
*Click pic to enlarge then if you still can't see it (not sure why it is still tiny and not full size) right click and push "open in new tab" and then click on the picture to "zoom in"
Wednesday, November 5, 2014
What is the Bayes' Theorem
"In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) relates current to prior belief. It also relates current to prior evidence. It is important in the mathematical manipulation of conditional probabilities. Bayes's rule can be derived from more basic axioms of probability, specifically conditional probability.
When applied, the probabilities involved in Bayes's theorem may have any of a number of probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. ln particular, with the Bayesian interpretation of probability, the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes's theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference.
Bayes's theorem is named after Rev. Thomas Bayes (/ˈbeɪz/; 1701–1761), who first showed how to use new evidence to update beliefs. Bayes' unpublished manuscript was significantly edited by Richard Price before it was posthumously read at the Royal Society. Bayes' algorithm remained unknown until it was independently rediscovered and further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 Théorie analytique des probabilités.
Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes's theorem "is to the theory of probability what Pythagoras's theorem is to geometry""
See more @ Wikipedia
More Info...
When applied, the probabilities involved in Bayes's theorem may have any of a number of probability interpretations. In one of these interpretations, the theorem is used directly as part of a particular approach to statistical inference. ln particular, with the Bayesian interpretation of probability, the theorem expresses how a subjective degree of belief should rationally change to account for evidence: this is Bayesian inference, which is fundamental to Bayesian statistics. However, Bayes's theorem has applications in a wide range of calculations involving probabilities, not just in Bayesian inference.
Bayes's theorem is named after Rev. Thomas Bayes (/ˈbeɪz/; 1701–1761), who first showed how to use new evidence to update beliefs. Bayes' unpublished manuscript was significantly edited by Richard Price before it was posthumously read at the Royal Society. Bayes' algorithm remained unknown until it was independently rediscovered and further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 Théorie analytique des probabilités.
Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes's theorem "is to the theory of probability what Pythagoras's theorem is to geometry""
See more @ Wikipedia
More Info...
Wednesday, July 30, 2014
Online Zoho notes about Math
Notes from my online Zoho account. Posting the saved file here since all the "notes" I need are now on this blog. Will not be updating these notes, what you see is what you get! :)
Notes
Notes
Thursday, June 26, 2014
Math in daily life @ Annenberg Learner
"When you buy a car, follow a recipe, or decorate your home, you're using math principles. People have been using these same principles for thousands of years, across countries and continents. Whether you're sailing a boat off the coast of Japan or building a house in Peru, you're using math to get things done.
How can math be so universal? First, human beings didn't invent math concepts; we discovered them. Also, the language of math is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Math can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race.
Join us as we explore how math can help us in our daily lives. In this exhibit, you'll look at the language of numbers through common situations, such as playing games or cooking. Put your decision-making skills to the test by deciding whether buying or leasing a new car is right for you, and predict how much money you can save for your retirement by using an interest calculator."
Check out Math In Daily Life @ Annenberg Learner
How can math be so universal? First, human beings didn't invent math concepts; we discovered them. Also, the language of math is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Math can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race.
Join us as we explore how math can help us in our daily lives. In this exhibit, you'll look at the language of numbers through common situations, such as playing games or cooking. Put your decision-making skills to the test by deciding whether buying or leasing a new car is right for you, and predict how much money you can save for your retirement by using an interest calculator."
Check out Math In Daily Life @ Annenberg Learner
Geometry lessons @ AAA Math
AAA Math's Geometry lessons includes:
Geometry is important and may be boring, but good to impress your crush with the knowledge of math.
Check out Geometry Lessons @ AAA Math
- Polygons
- Area
- Perimeter and circumference
- Volume
Geometry is important and may be boring, but good to impress your crush with the knowledge of math.
Check out Geometry Lessons @ AAA Math
Metric System conversion chart @ Merriam-Webster
Merriam-webster has a metric conversion chart to understand the differences between the units and how to convert them.
Check out the chart.
*Click pics to enlarge
Calculating Compound Interest
"First, the variables:
FV = future value
A = one-time investment (not for annuities)
p = investment per compound period
i = interest rate
c = number of compound periods per year
n = number of compound periods
To get p, take the target amount to invest each month, multiply it by 12 to get a yearly investment amount, then divide by c to get the investment per compound period. To get n, take the number of years to invest and multiply it by c to get the number of compound periods.
Simple compound interest with one-time investments... This is the formula that will present the future value (FV) of an investment after n years if we invest A at i interest compounded c times per year:
FV = A (1 + i/c)(n)
Required current investment (A) to have FV in the future if the i interest is compounded c times per year for n years:
FV
A = -----------
(1 + i/c)n
The time period (n) to have FV in the future if the initial investment A at i interest compounded c times per year:
ln(FV) - ln(A)
n = ------------------
ln(c + i) - ln(c)
NOTE: ln is the natural logarithm function.
Enter your own amounts:"
See exactly how to calculate compound interest
FV = future value
A = one-time investment (not for annuities)
p = investment per compound period
i = interest rate
c = number of compound periods per year
n = number of compound periods
To get p, take the target amount to invest each month, multiply it by 12 to get a yearly investment amount, then divide by c to get the investment per compound period. To get n, take the number of years to invest and multiply it by c to get the number of compound periods.
Simple compound interest with one-time investments... This is the formula that will present the future value (FV) of an investment after n years if we invest A at i interest compounded c times per year:
FV = A (1 + i/c)(n)
Required current investment (A) to have FV in the future if the i interest is compounded c times per year for n years:
FV
A = -----------
(1 + i/c)n
The time period (n) to have FV in the future if the initial investment A at i interest compounded c times per year:
ln(FV) - ln(A)
n = ------------------
ln(c + i) - ln(c)
NOTE: ln is the natural logarithm function.
Enter your own amounts:"
See exactly how to calculate compound interest
FinAid: Loan Calculator
" This Loan Payment Calculator computes an estimate of the size of your monthly loan payments and the annual salary required to manage them without too much financial difficulty. This loan calculator can be used with Federal education loans (Stafford, Perkins and PLUS) and most private student loans. (This student loan calculator can also be used as an auto loan calculator or to calculate your mortgage payments.)
This loan calculator assumes that the interest rate remains constant throughout the life of the loan. The Federal Stafford Loan has a fixed interest rate of 6.8% and the Federal PLUS loan has a fixed rate of 7.9%. (Perkins loans have a fixed interest rate of 5%.)
This loan calculator also assumes that the loan will be repaid in equal monthly installments through standard loan amortization (i.e., standard or extended loan repayment). The results will not be accurate for some of the alternate repayment plans, such as graduated repayment and income contingent repayment.
This loan calculator assumes that the interest rate remains constant throughout the life of the loan. The Federal Stafford Loan has a fixed interest rate of 6.8% and the Federal PLUS loan has a fixed rate of 7.9%. (Perkins loans have a fixed interest rate of 5%.)
This loan calculator also assumes that the loan will be repaid in equal monthly installments through standard loan amortization (i.e., standard or extended loan repayment). The results will not be accurate for some of the alternate repayment plans, such as graduated repayment and income contingent repayment.
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