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Dr Priti Bajpai
Приєднався 14 січ 2011
Prime Numbers an Introduction
In this video Prime numbers are first explained. It is shown how Sieve of Eratosthenes is used. Methods for finding a given number is prime or not are discussed. Polynomial time and time complexity is discussed. Some facts about primes are given and it is shown that there are infinitely many primes.
Notes, Practice problems and solutions can be found on my website
profpritibajpai.com
go to courses , check Number Theory .
#numberline #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#basicsofbinomialmadesimple#mathsforcomputerscience #Basicmathsforphysics #mathsformanagement#mathsforbiostudents
#mathsbasicsnotexplainedinclass# NumberTheory
00:00 Definition of Primes
00:37 Why are Prime numbers important and where are they used
01:27 Largest Prime
02:31 Fascination for Primes
02:45 Nature and Primes
02:56 Facts about Primes
04:22 Theorem
04:58 Primality Testing
06:58 Sieve of Eratosthenes
10:06 Finding if a given number is Prime or not by diving by Primes, Examples
12:56 Polynomial Time and Time complexity
14:40 Number of Primes upto a given number
16:06 Results about Primes
16:38 There are infinitely many Primes
19:36 Some things to note about Primes
Notes, Practice problems and solutions can be found on my website
profpritibajpai.com
go to courses , check Number Theory .
#numberline #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#basicsofbinomialmadesimple#mathsforcomputerscience #Basicmathsforphysics #mathsformanagement#mathsforbiostudents
#mathsbasicsnotexplainedinclass# NumberTheory
00:00 Definition of Primes
00:37 Why are Prime numbers important and where are they used
01:27 Largest Prime
02:31 Fascination for Primes
02:45 Nature and Primes
02:56 Facts about Primes
04:22 Theorem
04:58 Primality Testing
06:58 Sieve of Eratosthenes
10:06 Finding if a given number is Prime or not by diving by Primes, Examples
12:56 Polynomial Time and Time complexity
14:40 Number of Primes upto a given number
16:06 Results about Primes
16:38 There are infinitely many Primes
19:36 Some things to note about Primes
Переглядів: 35
Відео
Cramers Rule for Solving a System of Equations
Переглядів 25Місяць тому
In this video Cramers Rule is used to solve a system of equations. Limitations of Cramers rule are also discussed. Examples are taken to explain the concepts. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#basicsofbinomia...
Finding Inverse of a Matrix using Determinants Directly
Переглядів 16Місяць тому
In this video, Inverse of a matrix using Determinants is explained using examples. Minor, Cofactors, Transpose of a Matrix and Adjoint of a matrix is explained. A direct method along with the usual method is also explained for finding inverse. Notes, Practice problems and solutions can be found on my website www.profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #maths...
Determinants of order 3 and 4 made easy
Переглядів 652 місяці тому
In this video Determinants of order 3 and 4 are explained. First the value is found using expansion along first row, then different ways of writing the formula are explained. Then Sarrus rule for finding the value of the determinant directly is given. The value of the determinant of order 3 and volume of parallelepiped is also shown. Lastly how to find the value of a determinant of order 4 is e...
Determinants a New Approach
Переглядів 322 місяці тому
This video is about what are determinants , how are they added and subtracted. What are their properties and how we find the value of a second order determinant. Their connection to the area of a parallelogram. The next video in this series will be on order 3 and 4 determinants. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial ...
Inverse of a matrix using Elementary Row Transformations
Переглядів 182 місяці тому
In this video, Inverse of a matrix using Elementary Row Transformations is explained using examples. For a 2 by 2 matrix the formula is given and the method for finding inverse of matrices of any order is also explained. Notes, Practice problems and solutions can be found on my website www.profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #mathsbasics #engineeringmath...
Solving System of Equations using Elementary Row Transformations
Переглядів 183 місяці тому
In this video Solving system of equations is explained. First some important concepts like Pivot, Row Echelon Form , Reduced Row Echelon Form are explained with examples the problems are solved using the Elementary Row transformations and by reducing the augmented matrix to REF form. On related topic my other video can be checked for detailed explanations. ua-cam.com/video/-_j0g3mr_1A/v-deo.htm...
Matrices and Elementary Row Transformations
Переглядів 163 місяці тому
In this video Elementary row transformations are explained. Examples are taken to explain the three type of row transformations. These elementary row transformations will be used to expalin solving system of equations and for finding inverse of a matrix. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberline...
Matrix Multiplication
Переглядів 163 місяці тому
In this video Matrix Multiplication is explained in a simple way. Examples are taken to explain the Matrix Multiplication. Notes, Class lectures and Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#mathsforcomputerscience #mathsforbba #mathsf...
Matrix Operations
Переглядів 123 місяці тому
In this video Matrix operations like addition of Matrices, Subtraction of Matrices, Scalar Multiplication and Equality is first explained. Then Group properties of Matrices are explained. Notes, Class lectures and Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #mathsbasics #engineeringmathematics #mathlecture #mathmade...
Matrices an Introduction
Переглядів 253 місяці тому
This video gives an introduction to Matrices. Types of matrices are defined with examples. Where are matrices used is also discussed. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#mathsbasicsforbiostudents#mathsforcomput...
Problems on Vectors
Переглядів 264 місяці тому
This video is a continuation of 2 previous videos on vectors. Here all the concepts explained earlier are used to solve problems on vectors. Different types of examples have been taken for explanation of the concepts. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #mathsbasics #engineeringmathematics...
Vector Multiplication
Переглядів 174 місяці тому
In this video the multiplication of vectors is covered. Both the Dot and Cross product are explained with the help of examples. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberline #mathsbasics #engineeringmathematics #mathlecture #mathmadeeasy #mathmadesimple#basicsofbinomialmadesimple#mathsforcomputersci...
Basics Of Vectors
Переглядів 195 місяців тому
This video has all the basics of vectors. It explains different types of vectors and their representation. Vector addition using the parallelogram law of vector addition is also explained. In the next video Vector multiplication will be explained and then examples will be solved. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial...
Binomial Expansions
Переглядів 225 місяців тому
This video is in the form of a class lecture on Binomial Expansion. All the basic formulas are given and all different type of expansions which one can come across are discussed. It is a video which will clear all the doubts about how to expand Binomials. Notes, Practice problems and solutions can be found on my website profpritibajpai.com go to courses , check Remedial Mathematics . #numberlin...
Continued Fractions and solving Diophantine Equations
Переглядів 1636 місяців тому
Continued Fractions and solving Diophantine Equations
Continued Fractions , Euclidean Algorithm and Fibonacci Numbers
Переглядів 796 місяців тому
Continued Fractions , Euclidean Algorithm and Fibonacci Numbers
Arithmetic Series and Ancient Indian Mathematics
Переглядів 637 місяців тому
Arithmetic Series and Ancient Indian Mathematics
Solving Inequalities with Modulus function
Переглядів 297 місяців тому
Solving Inequalities with Modulus function
Operator Method for finding solution of differential equations
Переглядів 1579 місяців тому
Operator Method for finding solution of differential equations
Great Video. Nice refresher for me. I had completely forgotten some of this.
Thank you so much
u save my final:)))
be blessed,nice and helpful video
Thank you so much for the encouraging words
Excellent video. It was a great introduction. I wish we had such clear explainations when I was back in school and college.
Thank you so much. That is so encouraging.
The 1st question is incorrect....
It's typing error. The point is. ( 0, -3,,-3). Sorry guys
Sorry it is a typing error. The point is (0, -3, -3).
great video
Nice explanation ma'am...❤
Thank you so much. Thats very encouraging.
great video
Very good Mam !! Excellent lecture 👍👍
Thanks ma'am 🙏🏼
Thank you so much
Thank you, Ma'am, for such an insightful video on harmonic progression. Your clear and simple explanations truly make learning enjoyable 😊. I got transported back to my first year when I was in your remedial maths class. I really miss the feeling of looking forward to your lectures every week. Also, I love that you highlighted the real-life application in music -- makes me look at the abstract concept with newfound interest. Thank you for making math fun again for me ❤
Thank you so much. Your kind words make me feel it was worth the effort to make the video.
thx mam it helped me a lot for my quiz
Thank you so much and glad it helped you. Best wishes for your tests.
Excellent Professor
Top !
Thank you so much
Outstanding academic class
Excellent
How to check solution like 2/17=1 6/23=1 Explain this madam
2/17 is the legendre symbol. For 2/17 use the formula 2/p= (-1)^(p^2-1)/8 . p is prime. So 2/17 = (-1)^36 =1 For 6/23 first write 6/23= (2/23)(3/23) for 2/23 use above formula 2/23= (-1)^(23^2-1)/8 = (-1)^66 =1 For 3 /23 use 3/p =1 if p ≡ ±1(mod12) otherwise = -1. As 23 ≡ -1(mod12) 3/23 =1 Please check my video ua-cam.com/video/ExPjXxf63yk/v-deo.html on Legendre symbol for all formulas
please mention the mane of the theorem that you have used
I do not think the theorem has a name . It is proved using induction.
14:22 from where n1,n2 came😢
(I) m1=3, m2=5 these are modulus. M=m1 × m2 = 3×5 . Now n1= M/m1 and n2= M/m2 . I hope its clear
Very nice shared to others also
thank you for your great explanation ma'am. you really help me😊❤
9/13 =1 how? 2/17=1 Can sm1 say please
As (9/13) = 3^2/13 we used (a^2)/p =1 where p is prime. For 2/17 use the formula 2/p= (-1)^p^2-1 .So 2/17 = (-1)^36 =1
Madam (-1)^17^2-1= ? Please tell this madam
2/p= (-1)^(p^2-1)/8 . p is prime.
2/p= (-1)^(p^2-1)/8 .
great video
great video very well explained
❤
Than you
I'm very proud of you outstanding explanation
Thank you so much
very well explained
Thanks a lot for liking it.
Outstanding academic class
Thank you so much
🤩
Thank you for watching
Fine
Thank you for watching
Outstanding academic class
Thank you for watching
thanks a lot this was very clear and complete: nowhere else i've found tree methods for the resolution of a quadratic congruence!
Glad it helped! Thank you
Thank you 🌟
You’re welcome 😊
good video!
Thank you
Thank you, Professor. I have just discovered and subscribed to your channel. I hope that you are still making excellent videos like this one.
Thank you so much. Yes trying to.
Is there any method with O(1) complexity?
Try Hensel's Lemma
Can you explain the part where you introduce t, and how you go from 6(450) = 450-6t
Please check my video on solving diophantine euations in 2 variables. There I have explained how general solution is written in terms of a parameter t. Diophantine equations if solvable have infinite solutions and the different values of t give the infinite solutions
Thank you mam
Thank you for watching
thank you video i am not able to understand this in book as all question are given with using qdratic residue method which require more time ...ty
I hope it was useful
Nice class
Thank you
Nice
Thanks
Thanks for the video. I have two questions, if is possible: - how does it work the algorithm if a is even - how do you choose the y when solving xy = -b mod 2 ?
Not all quadratic congruence have a solution. For a even no solution will exist. You can check by giving different values to x the original congruence is never satisfied. put x=2 , 2^2-2 is not divisible by 2. 3^2 -2 is not sivisible by 2. ... As x is the initial solution, it is found from x^2 = a(mod2). Take an example if we are solving a congruence x^2 = 7(mod2), you can see x=3 satisfies . When we put x=3 in x^2 =a+ b2, gives 3^2 = 7 +b2 ,implies b=1 as x=3 and b=1 , xy= -b(mod2) is 3y=-1(mod2) solve this congruence. Here we can see y=1 satisfies so y=1
-3+164-7/14. = 11
yes thats correct should be 11. Typing error
Any job opportunity in Dubai mam? I have completed M.sc in Applied mathematics
Amazing mam 🌹❤️
thank you
I'm glad to found this video. Thank you very much
Glad it was helpful. Thank you.
how to eliminate y from the two equations?
Nevermind, I did it :D, make y=10-x and substitute in the first eq.
Need proof of the theorem
a|(bx +cy), therefore a|(bx +cy +fz +.....+nn) if it divides gcd. this is one of the first rule of divisibility, which is bezouts theorem
Very helpful! Thank you for sharing the step-by-step procedure in solving Diophantine Equation in Two Variables!
Thank you
Mam I have a problem that Prove that x^2 +y^2=z^2 With y even are x=r^2-s^2 , y=2rs , z=r^2+s^2 where r and see are arbitrary integers of opposite parity Can you prove it
Is this the way x^2 +y^2 = (r^2-s^2)^2 + (2rs)^2 = r^4 +s^4 -2r^2s^2 + 4r^2s^2 =r^4 +s^4 + 2r^2s^2 = (r^2+s^2)^2 =z^2