Math 254A (Number Theory)
This was the official course web page for Math 254A (Number Theory) at
UC Berkeley, which I taught in the Fall 2001 semester. The web page for
Math 254B is here.
The course description and syllabus for Math 254A
can be viewed here.
Note added 19 Jul 2002: all PostScript files are now compressed using
Gzip to save space.
Final exam info
The final exam was distributed in class Friday, November 30, and will
be due in my mailbox at 5 PM on Monday, December 10. It is also posted here
There will be no class
meetings at the scheduled time from this point onward. However, I will have
extended office hours during the week of December 3,
as follows: Monday and Friday 1-5 PM (with a break for
tea; find me in 1015 Evans), Tuesday 10 AM-1PM. At other times, send me email
and I'll respond as soon as possible. You can also contact Frank with
Final exam corrections
- 3: should refer to Problem Set 4.
- 7: Assume that K is not L.
- 10: in (a), the degree should be 6, not 5, or else the other parts
will not work.
For the professor
757 Evans Hall
Office hours: Monday and Thursday 1-2 PM, or by appointment, or just drop by.
If the door is open, come right in; if not, go ahead and knock, but I reserve
the right not to answer.
I'm usually in my office immediately after lecture, and generally during
late morning (before noon) and early afternoon (until 3 PM).
I'm often at tea in 1015 Evans from 3 to 4 PM.
I also will respond
to questions by email, usually even over the weekend.
For the teaching assistant
1010 Evans Hall
Office hours: Wednesday and Friday 2-3 PM. Frank is also often at tea from
3 to 4 PM.
I'm willing to be flexible about late homeworks
if you let me know in advance what the difficulty is and when you
expect you'll be able to get the homework in. (Sending me an email over the
weekend will usually satisfy this requirement, though earlier notice, say
in class on Friday, is better.) I'm not trying to be an ogre
about deadlines: I'm just trying to make sure no one falls behind,
which is usually the kiss of death in a course like this.
Some problems on the homework contain references to, or request code to be
written in, the computer algebra package Magma. To run Magma on the Berkeley
math department systems, type magma at any Unix prompt. (If you
don't have access to the math department systems, see me and I'll see what
I can do about getting you such access.)
The Magma home page
documentation; the same documentation can also be found in the folder
/usr/local/Magma on the department network.
Print copies of the Magma manual can also be found in
room 708S (adjoining the computer cluster); please do not remove these.
Magma is not free software, but the math department has a site license. This
means it is possible for department affiliates (or non-affiliates enrolled
in a course using the program) to install Magma on their own
computers. See Paulo Ney de Souza or one of the other computer staffers on
the 9th floor for details.
Warning: corrections have not been made to these files. See here for corrections.
- Solution set for Problem Sets 1 and 2: TeX,
- Problem Set 1 (due Sep. 5): TeX,
- Problem Set 2 (due Sep. 10): TeX,
- Problem Set 3 (due Sep. 17): TeX,
- Problem Set 4 (due Sep. 24): TeX,
- Problem Set 5 (due Oct. 1): TeX,
- Problem Set 6 (due Oct. 8): TeX,
- Problem Set 7 (due Oct. 15): TeX,
- No problem set due Oct. 22.
- Problem Set 8 (due Oct. 29): TeX,
- Problem Set 9 (due Nov. 5): TeX,
- Problem Set 10 (due Nov. 14): TeX,
- Problem Set 11 (due Nov. 21): TeX,
- Final Exam (due Dec. 10): TeX,
- August 27 (Mon): TeX,
- August 29 and 31 (Wed/Fri): TeX,
- September 5 and 7 (Wed/Fri): TeX,
- September 10, 12 and 14 (M/W/F): TeX,
- September 17 and 19 (M/W): TeX,
- September 19 (Wed) supplement: TeX,
- September 21 and 24 (F/M): TeX,
- September 26 (Wed): TeX,
- September 28 (Fri): TeX,
- October 1 and 3 (M/W): TeX,
- No new handout October 5: continuation of the previous handout.
- October 8 and 10 (M/W): TeX,
- October 12 (F): TeX,
- No classes October 15, 17, 19.
- October 22 and 24 (M/W): TeX,
- October 26 (F): TeX,
- October 29 (M): TeX,
- Supplement on the relative discriminant: TeX, DVI, PostScript
- October 31 (W): TeX,
- No class November 2.
- No new notes November 5 or 7; continuation of the previous handout.
- November 9 and 14 (F/W): TeX,
- No class November 12 because of the Veterans' Day holiday.
- No new notes November 14 or 16: continuation of the previous handout.
- November 19 and 21 (M/W): TeX,
- No class November 23 because of the Thanksgiving holiday.
Required: undergraduate algebra (Math 113 or equivalent). Possibly
helpful: graduate algebra (Math 250 or equivalent). More
specifically, we will use basic facts about groups, rings, fields, and
Galois theory. Also possibly helpful: some familiarity with classical
For the most part,
I will be following the recent English translation of Jürgen
Neukirch's Algebraic Number Theory, published by Springer-Verlag.
I have designated this a "recommended" text, rather than a "required" text,
only because of its steep price tag. I also plan to distribute lecture
notes, though these may lag slightly behind the lectures.
Other books worth looking at for various reasons are:
- Borevich and Shafarevich, Number Theory
- Cassels and Fröhlich, Algebraic Number Theory
(just the early chapters, for starters)
- Fröhlich and Taylor, Algebraic Number Theory
- Ireland and Rosen, A Classical Introduction to Modern Number
Theory (for background)
- Janusz, Algebraic Number Fields
- Marcus, Number Fields (lots of examples)
- Pollard and Diamond, The Theory of Algebraic Numbers
(assumes minimal prerequisites)
Number Theory Seminar meets Wednesdays from 3:10 to
4:00 PM in 891 Evans, and sometimes on Friday at the same time and place.
Prospective students in number theory are encouraged to attend.
If you're shopping for an advisor in number theory,
check out the Web pages of
Ken Ribet, and
Some more possibly useful links:
- J.S. Milne has
printable notes from a variety of courses, including Algebraic Number Theory.
- The Number Theory
Web is the home of all things number-theoretic on the Web.
Kiran S. Kedlaya (kedlaya[at]math[dot]mit[dot]edu)


3 edition of Recent progress in analytic number theory found in the catalog.
Recent progress in analytic number theory
|Statement||edited by H. Halberstam, and C. Hooley.|
|Contributions||Halberstam, H., Hooley, C., 1928-, London Mathematical Society., LMS Durham Symposium.|
|LC Classifications||QA241 .R35 1981|
|The Physical Object|
|Pagination||2 v. ;|
|ISBN 10||0123182018, 0123182026|
|LC Control Number||81066693|
Every rational number 2Q ˆC is obviously an algebraic one. More-over, as we will see later, a rational number is an algebraic integer if and only if it is an integer. Exercise (1)Prove that p 2 and 1 2 + p 3 2 are algebraic in-tegers. (2)Prove that if 2C is an algebraic number then Re and Im are algebraic numbers. Whether the same. A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Stopple, Jeffrey, – A primer of analytic number theory: from Pythagoras to Riemann / Jeffrey Stopple. p. cm. Includes bibliographical references and index. ISBN – ISBN (pb.) 1. Number Cited by:
A more recent version may be available at Mathematics» Analytic Number Theory» Lecture Notes These lecture notes are the only required reading for the course. Apostol, T.M. Introduction to Analytic Number Theory Springer £ - ISBN This book is Print on Demand and can be ordered through any bookseller. Please allow .
O. Forster: Analytic Number Theory 1. Divisibility. Unique Factorization Theorem Deﬁnition. Let x,y∈ Z be two integers. We deﬁne x| y (read: xdivides y), iﬀ there exists an integer qsuch that y= write x- y, if this is not the case. We list some simple properties of divisibility for numbers x,y,z∈ Z. Remember it is ANALYTIC number theory, so it is more concerned with deriving proofs, rather than stating them for the general reader. Apostol's exposition and writing style does half the magic. For a general book on Number Theory try Ogilvy or for basic introduction into proofs of Number Theory try GA Jones or Dudley/5(47).
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Joey Dee gets wise
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Attachment and bonding
Reed-Robins family of the Southeastern United States
The Peters family
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A vvedding sermon preached at Bentley in Darby-shire
Jack Goldstein x 10,000
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Principles of the theory of solids.
Recent Progress in Analytical Number Theory, Two-Volume Set: Recent Progress in Analytical Number Theory: Volume 1 (Recent Progress in Analytic Number Theory) by Author Unknown (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or.
Get this from a library. Recent progress in analytic number theory. [H Halberstam; C Hooley; London Mathematical Society.;] -- The papers presented in these two volumes were presented at the Durham Symposium of the London Mathematical Society, which was held on the campus of Durham University between July 22 and August 1.
Full Description: "An undergraduate-level introduction whose only prerequisite is a standard calculus course. A Primer of Analytic Number Theory, making writing skills is in line with your capacity: Exposure to published, written works has greatly influenced his writing, as other writers rhythm, flow and observed style of writing, always affect your work.
The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Key topics and features: various lower bounds on the complexity of some number theoretic and cryptographic problems, associated with classical Recent progress in analytic number theory book such as RSA, Diffie-Hellman, DSA as 3/5(1).
Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking.
Talks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory. The present book is the Proceedings of these two conferences, which records mainly some recent progress in number theory in China and Japan and reflects the academic exchanging between China and Japan.
The Mathematical Sciences Research Institute (MSRI), founded inis an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions.
The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the.
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
It is often said to have begun with Peter Gustav Lejeune Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.
It is well known for its results on prime numbers. ANALYTIC NUMBER THEORY | LECTURE NOTES 3 Problems Siegel's Theorem * Some history The prime number theorem for Arithmetic Progressions (II) 2 38 Goal for the remainder of the course: Good bounds on avera ge Problems The Polya-Vinogradov Inequality Problems Further prime.
This site is like a library, you could find million book here by using search box in the header. Analytic Number Theory Solutions Sean Li Cornell University [email protected] Jan. Introduction This document is a work-in-progress solution manual for Tom Apostol’s Intro. international gathering of leading number theorists who reported on recent advances in both classical analytic number theory as well as in related parts of number theory and algebraic geometry.
It is our hope that the legacy of Gauss and Dirichlet in modern analytic number theory is apparent in these proceedings. Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N.
Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit, MIT Press, August ; Automorphic Forms and Representations, D. Bump, CUP ; Notes on Fermat's Last Theorem, A.J.
van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced. mation about number theory; see the Bibliography. The websites by Chris Caldwell  and by Eric Weisstein  are especially good. To see what is going on at the frontier of the subject, you may take a look at some recent issues of the Journal of Number Theory which you will ﬁnd in any university library.
Contemporary number theory is developing rapidly through its interactions with many other areas of mathematics. Insights from ergodic theory have led to dramatic progress in old questions concerning the distribution of primes, geometric representation theory and deformation theory have led to new techniques for constructing Galois representations with prescribed properties, and the study of.
ISBN: OCLC Number: Notes: "Based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June"--Page 4 of cover. A Classical Introduction to Modern Number Theory: Edition 2 - Ebook written by Kenneth Ireland, Michael Rosen. Read this book using Google Play Books app on your PC, android, iOS devices.
Download for offline reading, highlight, bookmark or take notes while you read A Classical Introduction to Modern Number Theory: Edition /5(2).
Introduction to Analytic Number Theory - Ebook written by Tom M. Apostol. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Introduction to Analytic Number Theory.
Abstract. There has been much progress in recent years on some classical questions in analytic number theory. This has been due in large part to the fusion of harmonic analysis on GL(2,R) with the techniques of analytic number theory, a method inspired by A.
Selberg .A lot of impetus has been gained by the trace formula of Kuznetsov , , which relates Kloosterman sums with Author: Dorian Goldfeld, Dorian Goldfeld, Dorian Goldfeld. Kolesnik, On the estimation of multiple exponential sums, in Recent Progress in Analytic Number Theory, Symposium Durham, Academic, London,1(), A short interval result for the Smarandache ceil function and the Dirichlet divisor function.
Analytic Number Theory: count the solutions. – (Gauss circle) What is the average number of ways to represent an integer at most x as a sum of two squares. – (Roth) Let A be a dense subset of [n]. Then A must have many solutions to x+z =2y. – Primes å(Mertens) p x 1 p =loglogx+C+O(1 logx).
å(Gauss; Riemann+dvP/Hadamard) p x logp=x+O. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.
Problems in Analytic Number Theory Author: M. Ram Murty Published by Springer New York ISBN: DOI: / Includes bibliographical references (pages ) and index "This book gives a problem-solving approach to the difficult subject of .Analytic Number Theory By H. Rademacher Notes by K.
Balagangadharan and V. Venugopal Rao Tata Institute of Fundamental Research, Bombay Contents I Formal Power Series 1 1 Lecture 2 2 Lecture 11 3 Lecture 17 4 Lecture 23 5 Lecture 30 6 Lecture 39 7 .


I sent you a topic list last night and now we have some practise papers designed just to practise paper 3 next Tuesday for all year 11.
The links are included below and I have put them all on show my homework.
So far the maths exams have been much more accessible for pupils than last year. Some of the maths may be hard but as long as the questions are accessible for the pupils then that is the main thing. I wish them every success in their last paper
Many thanks for your continued support over this stressful time for all the young people.


I have successfully wired the motors so that they run ... and run ... and run until I either click on stop or the bCNC just gives up and says the world is coming to an end.
One of the things I need (I think) is to set $100,101 and 102. If I'm reading it correctly, this tells GRBL how many steps it takes to one mm. The equation is: Steps/mm = (Steps per Revolution)*(Microsteps) / (mm per Revolution)
(http://www.diymachining.com/downloads/G ... _Rev_B.pdf).
From the people who sold me the motors:
1) Z will move 12.7mm per revolution (200 steps), X and Y will move 29.263mm per revolution (200 steps).
I have my external drivers set to 800 steps/rev. If I'm doing it correctly this would be:
800/29.263 = 26.999... Essentially, 27 steps for one mm on X and Y.
800/12.7 = 62.99... 63 steps for one mm on Z
This seems weird. Is this correct?
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Welcome to Year 4!
This year the people helping us are Mr Scarr, who is our teacher, and Mrs Gillard, who is our LSA.
A very exciting beginning to the spring term as the children have many interesting topics to learn. Read below to find out what's in store for year 4 this term. #onlythebest.
Please follow me @MrScarrMLP on twitter. I will be updating my twitter page daily with some of the fantastic work year 4 have been producing.
In English, we will be learning all about El Dorado. The children will have an opportunity to write a diary entry, a letter and a play script as well as filming each part every Friday.
In Maths, we will be focusing on fractions and measurement. The children will identify equivalent fractions and solve addition & subtraction problems based on the real world.
In Science, we will be learning all about electricity. This is the first time the children will have learned about electricity, they will have the chance to build a circuit and identify any errors within a faulty circuit.
In Geography, we will be learning all about Europe and examining some of the physical and human features of the continent. Then we will look at Leisure and Entertainment in the 20th Century.
In RE, we have been looking at worship and how Christmas is celebrated around the world. This term we will be looking at commitment and the life of Jesus in the run up to Easter.
PE will be on a Monday and Wednesday every week. Please make sure all PE kits are in school the first week back. We are looking at creating a routine in gymnastics


• Transversal … a line that intersects 2 others.
(e.g.) The red line in Figure 1
• Vertical Angles
… The opposite angles formed by two intersecting straight lines.
(e.g.) a and d in Figure 1 (b and c, e and h, g and f in Figure 1 are also the vertical angles.)
• Corresponding Angles
… a pair of angles at the same location at each intersection.
(e.g.) a and e in Figure 1 (b and f, c and g, d and h in Figure 1 are also the corresponding angles.)
• Alternate Interior Angles
… a pair of angles inside the parallel lines on opposite sides of the transversal.
(e.g.) c and f, d and e in Figure 1 are the alternate interior angles.


GSEB 12th Math Solution / Objective Answer 2019
Gujarat Secondary and Higher Secondary Education Board (GSEB) is going to take Mathematics examination around the Gujarat on 14th March 2019. All the students who have applied for appear in the Gujarat Board Inter Examination 2019 will participate in the exam at their respective Examination Center.
Gujarat Board 12th Math 2019 Objective Answer
After appear in the Gujarat Board Class 12th Math Exam students first of all they will like to calculate how many objective Questions answer they have given correctly hence they surely try to find Gujart Board 12th Math (050) Objective Answer for their set. On this website we will update Gujurat Board Class 12th / GSEB HSC 12 Maths (050) Answer key 2019.
GSEB XIIth Math Objective Answer Update
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Gujarat Board GSEB Inter Math MCQ Solution 2019
Board: Gujarat Secondary and Higher Secondary Education Board
Class: HSC (12th)
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Exam Date: 14/03/2019
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On this page, I will go over what I wrote on my senior thesis. I only extract key research ideas and figures from my thesis. To view the full version of my senior thesis, click here. To view the matlab code, please go to my github repo.
Keywords: adaptive subspace identification, dynamic tracking, state-space models, forgetting factor, prediction error, tracking error.
Through identifying and tracking of brain network dynamics, neuroscientists have been able to understand neural mechanisms in a deeper level for the past decades. A broad range of neurological disorders can be effectively treated by developing adaptive closed-loop stimulation therapies or brain-machine-interface (BMI). They utilize real-time neural signal monitoring and brain states control using electrical stimulation. However, due to the non-stationary and time-variant properties of some brain network dynamics, such modeling becomes challenging.
In this work, we implement an adaptive subspace identification algorithm (subID) developed by yang et. al.1 and test it on simulated time-invariant and time-varying state-space models (SSMs). We run some simulations to prove that the algorithm can track the poles trajectories of the time-varying State-space models in an adaptive manner with high accuracy. By quantifying the performance with prediction error and tracking error, we experimentally show that the proposed adaptive identification algorithm could better predict and track poles of the true time-varying system, as compared to the traditional non-adaptive identification algorithm.
We first formulate time-varying SSMs of purely stochastic systems as
where \(x\) is the hidden state, \(y\) is the observation state, \(A\) and \(C\) are time-varying system matrices, \(K\) is the forward Kalman gain, \(e_t\) is a noise set to zero mean with variance of 0.0001. In our experiments, we set our system to a second order with zero inputs and two outputs. \(A\) is the only time-varying matrix with changing diagonal elements in each time steps, with absolute value of all poles of \(A\) less than 1 (stability requirement). The \(C\) matrix is set to an identity matrix.
We adapt our adaptive subID algorithm from the original time-invariant subID algorithm from Overschee’s book (a good introduction to subID)2. To make the algorithm adaptive, we introduce a user-defined forgetting factor, β, to estimate time-varying output covariance matrices,1
Here, we update the estimate of output covariance matrices at each time step, while putting more weight on the recent data than past data. A small β implies the recent data are more heavily weighted, and a large β implies the past data are weighted almost as heavy as the recent data. β = 1 means that the entire dataset is weighted equally, which is equivalent to the non-adaptive output covariance matrices.
Since we calculate new output covariance matrices using QR-decomposition, and that they are updated at every time step, we need to recalculate QR matrices at every time step. To enable an efficient, online operation of the QR-decomposition, we use a recursive algorithm to update the R matrix in the QR-decomposition 1 with the help of Givens rotation (check out
qrinsert.m in Matlab). I will leave the math details in my thesis.
Training and testing sets
We allocate the 5500 time steps into 5000 for training and 500 for testing. The adaptive algorithm estimates the SSM at each time step of the training set. During training, we record the estimated poles of the time varying system at each time step to investigate the pole tracking ability of the algorithm. We fix SSM_adpt at the last estimate. The non-adaptive algorithm uses the entire training data to produce a single estimation, SSM_non-adpt. Using SSM_adpt and SSM_non-adpt, we evaluate the prediction power on the testing set, which is unseen by both algorithms. We do not further adapt the SSM_adpt during testing. We compare these predictions to the baseline, which is defined as the true SSM at the last time step of the training set.
We introduce two error metrics to evaluate the algorithm’s performance. We quantify 1) a prediction error (PE), using a normalized root mean square error between the predicted outputs and the true outputs in the test set, and 2) a tracking error (TE), also using a normalized root mean square error between an averaged estimated and the true eigenvalues of the TV matrix at each time step.
One thing to note is that we take the mean and standard error of the mean (SEM) of PE of all 200 Monte Carlo simulations, but we perform TE on the averaged pole trajectories over all Monte Carlo simulations, instead of on individual simulations, which have estimated poles with very large variance. We then take the mean and SEM of TE across all poles. The exact equations of the error metrics are in my thesis.
For each case, we visually evaluate the pole tracking ability of the adaptive algorithm and compare the output estimation in the test set. We also quantitatively compare PE and TE of both algorithms.
Since this is a time-invariant system, we set β = 1 to show that the adaptive algorithm can perform equally well when all past data are used. The pole estimation using the non-adaptive algorithm can perfectly track the true time-invariant poles and the estimated poles using adaptive algorithm can converge quickly to the true poles as well.
For all time-varying cases, we can point out that the non-adaptive algorithm fails to track the poles trajectories over time. Even when the non-adaptive algorithm uses all past data, since only one estimated system is produced, it is impossible to track poles in an adaptive manner. On the other hand, the adaptive algorithm can effectively track the true poles of the time-varying system. In figure (b), the estimated outputs of the test set using the adaptive algorithm are also closer to the true outputs compared to the non-adaptive algorithm. Judging visually, we can already conclude that the adaptive algorithm has a higher estimation power in the simulated time-varying cases.
We also want to compare the algorithms quantitatively using our defined error measures. For all time-varying cases, we obtain TE_adpt < TE_non-adpt and PE_baseline < PE_adpt < PE_non-adpt, proving that the performance of the adaptive algorithm is indeed better than the non-adaptive algorithm. Meanwhile, adaptive algorithm can perform equally well as the non-adaptive algorithm in the time-invariant case.
Influence of the forgetting factor
One goal of the project is to determine the best value of the forgetting factor, β . The figure below displays the pole trajectories of some time-varying cases as β increase from 0.8 to 1. Remember, larger the value of β, heavier the past data are weighted. A β = 1 means that the entire dataset is weighted equally.
For β = 0.8, the pole trajectories of all cases are poorly estimated with large estimate variance. As the value of β increases from 0.8 to 0.98, the algorithm starts to perform more accurately in tracking poles. The estimate variance is also reduced as the value of β gets close to 1. When β = 1, the algorithm cannot track any time-varying part of the system in all cases, because the weights on past data equal to the weights on the recent data.
The performance of the algorithm with β = 0.98, 0.99, and 0.995 is very similar in terms of pole tracking, but there is a difference in terms of rate of convergence to the true poles. Closer the value of β to 1, more recent data are weighted in the algorithm, so longer it takes to converge to the true poles. As the value of β increases from 0.98 to 0.995, we can see an increasing delay in pole convergence in the random walk case and a slower convergence in the step function case. In real-life scenarios, maintaining a quick rate of convergence is surely something scientist concerns.
My thesis has more contents that I didn’t get to cover here. To be specific, we investigate the effect of the forgetting factor and training set length empirically (with error measures) to best optimize our simulations. I also encourage you to read the details of the algorithm in the method section.
Y. Yang, E. Chang, and M. Shanechi, “Dynamic tracking of non-stationarity in human ECoG activity,” Proc. IEEE Engineering in Medicine and Biology Society Conference(EMBC), Jeju Island, Korea, pp. 1660–1663, 2017. ↩ ↩2 ↩3
P. Overschee and B. Moor, Subspace Identification for Linear Systems: Theory, Implementation, Applications, vol. 3. Kluwer academic publishers Dordrecht, 1996. ↩


Add weight values/make flexible
Currently, issue weight only supports values 1-9. Many companies utilize much higher numbers, especially Fibonacci numbers when doing scrum planning. I saw some discussion in the original issue (#70 (closed)) about this and I'm not sure where the discussion ended up regarding 1-9 vs. other. Can we make this more flexible by either having a number field that the user can use to enter any number, or can we add up to 100 (at least) in the select list? Since it's a select2 field it is easy to type higher number in that will auto-select up to 100 or X max value.


At St Kentigern’s Catholic Primary School we believe that, from a very early age, mathematics is a vital part of children’s development throughout school. Children’s chances of success are maximised if they develop deep and lasting understanding of mathematical procedures and concepts. We value a curriculum that is creative and engaging and follows a mastery approach. Mastering maths means pupils of all ages and abilities acquiring a deep, long-term, secure and adaptable understanding of the subject.
Mathematics is the foundation for understanding the world and our aim is that children know the purpose behind their learning and how to apply their knowledge in their everyday lives. We strive to give children the chance to believe in themselves as mathematicians and develop the power of resilience and perseverance when faced with mathematical challenges. Children will make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They will become fluent in mathematics that can be recalled quickly and transferred and applied in other subjects.
At St Kentigern’s we follow White Rose planning in order to ensure that our children have full coverage of the Mathematics National Curriculum and to allow our pupils to build upon topics; embedding concepts. Children are taught through clear modelling and have the opportunity to develop their knowledge and understanding of mathematical concepts. The mastery approach incorporates using objects, pictures, words and numbers to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding at all levels. All children are catered for within the maths lessons, ensuring that the teacher and support staff offer the necessary support and challenge for each individual to make progress.
We ensure that mathematics is taught in creative and engaging lessons using a wide array of maths manipulatives to aid and support our pupils in their learning. We aim to encourage the deepest of learning for our children so that their knowledge can be transferred and applied in many contexts including other subjects and their everyday lives. Pupils work on the objective at whatever entrance stage they are assessed as being at and they can acquire the skill, apply the skill or deepen the skill within the lesson. Children move through the different stages of their learning at their own pace and those who have shown their understanding at a deep level within the unit of work, will have opportunities to apply these skills in a greater depth activity. This should be challenging and ensure that children are using more than just one skill to be able to answer the mathematical problems. Reasoning and problem solving are integral to the activities children are given to develop their mathematical thinking.
Mathematics is widely valued across school and our classrooms have working walls that the children can utilise to support their learning and provide extra challenge.
We aim to ensure that the three core areas of the National Curriculum are covered in our lessons: fluency, reasoning and problem solving. We aim to offer opportunities for varied and frequent practice of maths skills with a focus on the ability to recall and apply their knowledge quickly and accurately. Mathematical vocabulary is a vital part of each lesson and the pupils need to be able to understand this in order to make links and connections with other areas of this subject. We hope to build confident mathematicians who have a love of maths, good problem-solving skills and a resilience that they can use in all aspects of their learning and day-to-day lives.
Through our creative and engaging maths curriculum we aim to show a clear progression in work throughout school and enable all children to:
- Use and apply the skills and knowledge learnt and to transfer these to other subjects and everyday life.
- Have an enjoyment of mathematics and relish solving problems and puzzles.
- Build up resilience and perseverance which will be beneficial in all areas of children’s lives.
- Reach their mathematical potential by being consistently challenged at an appropriate level.


Here, in the United States, achievement test scores in math and science are second-rate and falling with respect to many other countries of the world. Why is this happening? To say that the reasons are several and complex would be a true statement – to a point. A thorough examination of the reasons for America’s declining performance reveals a common-thread: A lack of common-sense in the way we both educate… and raise our children to have a “learning attitude.” A learning attitude and the foundation for success in school comes from home.
My upcoming book (available in October), Nurturing Curiosity and Success in Science, Math, and Learning highlights many of the issues at play while offering concrete suggestions to parents, mentors, and even teachers on how to “right the listing ship” of learning at the national level.
My book is not primarily concerned with our national achievement rankings, however; its prime focus is on helping parents and mentors at home partner with the schools to improve their student’s school performance and future prospects. The book addresses all aspects of learning and student motivation while paying special attention to those typically troubling subjects, science and mathematics.
To illustrate one of the many approaches I advocate for parents, mentors, and educators, Chapter 5 in the book presents “The Lottery Prize Choice.”
Beginning of Book Excerpt:
The important point is this: Some facility with mathematics is crucial to an intellectually rich and materially prosperous life … for most of us. The more math you know, the greater the potential rewards in life, monetary and otherwise. It is our task as student mentors to first convince ourselves that this is true. Only then can we proceed to make a convincing case to our students. Perhaps you have tried simply telling your student that “math is important; you need to know it!”…and that got you nowhere!
I advocate a subtler, common-sense approach, appealing to students’ curiosity and their inexperienced instincts by using real-life examples instead of merely preaching the virtues of mathematics for getting a good job someday, being successful, etc.
To illustrate my point, consider the following example which seems appropriate in this age of mega-million lotteries:
The Power of Math: The Lottery Prize Choice
Congratulations! You just won the local lottery. You are given the choice of two prize options:
Option 1: $10,000 in cash – paid immediately!
Option 2: One penny in cash – paid immediately! But hold-on, there is the proverbial “fine print” attached to option 2: The town banker has consented to hold your penny in the bank and pay you an interest rate on that penny of 1% compounded and applied daily for a maximum of five years. At that time, or any time sooner upon your request, you will be paid the total accumulated amount in cash.
A Note on how the “compound interest” in option 2 works: The winner gets one penny at the awards ceremony and promptly deposits it in the town bank. The next day, the penny earns 1% interest (one one-hundredth of a penny) which is added to the original penny. Now the prize is worth 1.01 cents (1 plus 1 times 0.01). The next day, the 1.01 cents earns another 1% interest on itself which makes the total holding equal to 1.0201 cents (1.01 plus 1.01 times 0.01). This continues every day for five years.
The $64,000 question: Which option do you choose?
If you choose option 1, you will be sorry! Yes, you will have $10,000 in cash in your pocket – immediately. That can buy a lot of neat stuff like computers, stereos, smart-phones, a trip to Disneyland!
If, on the other hand, you had an understanding of the mathematics of finance – merely basic math in this case coupled with some mathematical reasoning ability, you certainly would choose option 2, wait five years and collect your $770,000 penny-accumulation!
Just imagine what that could buy? How about some Ferrari automobiles, the best college education, a beautiful new home, your future retirement, and/or ….?
Of course, it is unlikely the town banker would ever offer such a deal, but the example emphasizes to anyone, the power of mathematics – even the basic mathematics employed above. The calculation involved in this problem is simple, easily done on any student calculator. The solution to the problem – coming up with the right decision – requires a respect for the power of numbers which one obtains given a minimal dedication to the study of math.
Here, in this example, is a great illustration of the old adage, “knowledge is power,” and, despite the unrealistic premise of the generous banker presented in option 2, the lesson of this example is not far removed from the many problems recent home-buyers faced due to their poor understanding of mortgage finance and interest rates.
We have focused on mathematics in our discussion so far in this chapter and in the above example for no other reason than its importance to science and to a complete education. The lottery prize problem is but one example of a real-world, hands-on, approach which can be effective at generating student curiosity and interest in the possibilities of mathematics. This book will often emphasize the close relationship between science and mathematics while continuing to stress, as well, the importance of math alone in finance, statistics, and everyday life.
End of Book Excerpt!
Appendix 1 in the book illustrates the simple math involved in the problem for the benefit of parents and mentors.
Two overriding messages are presented and developed within my book:
– We often look in all the wrong places for ultimate solutions to math, science, and learning problems: “Better” schools, “better” teachers, more class time, and more technology in the classroom are not the ultimate answers.
– A “learning attitude” begins at home: Nurturing a real curiosity and interest within students about the wonderful world which surrounds them demands some common-sense insights and practices from parents and mentors. Such an approach is the true key to success. As Albert Einstein once insisted, “I have no special talents. I am only passionately curious.” And he was.


Mathematical Physics. Front Cover. H K Dass. S. Chand, - Science - pages. 10 Reviews. Mathematical Physics. Get Textbooks on Google Play. Rent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone. Go to Google. The interest show for the title Mathematical Physics by the students has encouraged me to upto-date the fernlowlitiltsi.ga edition has been updated by the addition of.
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Zill's Advanced Engineering Mathematics is a compendium of topics that are most often covered in courses in engineering mathematics, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations, to vector calculus, to partial differential equations.
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Compound interest is an essential concept to understand when balancing the forces of investing and borrowing. It gives you the ability to make stronger money moves. Albert Einstein said compounding interest is the eighth wonder of the world and one of man’s greatest invention.
What is the true definition of an compound interest?
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It’s thought of as interest on interest.
Compound interest can work for you in your investments or it can work against you if you are repaying debt, especially high interest rates, such as credit card debt. When working for you compounding interest in investments can be a potent factor in growing your money. In the video below, Kevin talks about the basics of compounding interest and how it works.
Watch the video below:
Hi Everyone! My name is Kevin Major and today we’ll talk about Compounding interest. Compound interest or compounding interest is the interest calculated on the initial principle and also the accumulated interest of the previous periods of the deposit or loan.
You can think of this as interest on interest. To better understand compound interest let’s go through a couple examples. Say you have credit card debt or student loan debt you know you have to pay interest towards the company that’s lending you the money, but what you might not know is how often that interest is reviewed or how you’re paying it. The interest could be reviewed on your account on a ongoing, monthly, quarterly, semi-annual, annual basis and every time you’re making a payment towards this account you’re paying a little bit towards the principle as well as a little bit towards the interest while what you might not know is if you’re making the minimum required payment to these accounts you might be making a payment that’s less than the accumulated interest. So on the next month’s payment not only are you paying interest on the principle you’re still borrowing but you’re paying interest on the outstanding interest on the previous period. Another way to look at this would be an investment or 401(k) account where you have compound returns. You know you’re putting money into the account and you know you’re seeing market performance but what you might not know is for every day you see positive growth not only are you receiving money from returns from the money you put into your account but you’re also receiving returns on all the previous growth you’ve seen.
Hopefully this has helped give you a better understanding on what compound interest is and more money advice and resources check out MoneyNav.


August 31, 2012
Sounds like one of those math concepts. Equivalency or something. But really, we don’t think about math much around here. Not that that isn’t fun, it is; it’s just, all things being equal, we have to balance our time thinking about things.
And so we’ve focused on just one thing of late: a new episode of The Mikie Show!
Yes, we’ve all come to the same place at the same time, together! Just click the first word you hear in the first sentence and we’ll join hands, left and right, in a binary subset of first-rate entertainment!
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In the wondrous realm of education, where young minds embark on thrilling journeys of discovery, the alchemical fusion of amusement and enlightenment yields a transformative elixir. This elixir possesses the remarkable power to transmute the ordinary into the extraordinary, igniting a sense of wonder and curiosity that propels learning to new heights. One such enchanting avenue in this grand odyssey of education is the realm of maths dice games. When wielded with creativity, enthusiasm, and a sprinkle of imagination, these games become a gateway not only to unravelling the mysteries of complex mathematical concepts but also to fostering an environment of joy and camaraderie at home. Within the pages of this comprehensive guide, we embark on a captivating odyssey through an extensive array of fun maths games with dice. These games, like constellations in the night sky, seamlessly weave the threads of education and entertainment, igniting sparks of curiosity and excitement for mathematics that will illuminate the hearts of players and leave an indelible mark on their learning journey.
The Allure of Math Dice Games: Where Learning Meets Play
In the labyrinth of education, where textbooks and assignments can sometimes invoke weary sighs, maths games to play with dice appear as a breath of fresh air. They unravel a tapestry where learning and playing dance harmoniously, inviting learners to step into the roles of explorers, strategists, and even storytellers. Through these immersive games, players embark on quests that transcend mere learning and become captivating adventures where the treasures sought are not gems or gold, but the gems of knowledge and mastery over mathematical concepts. The allure of maths games using dice lies in their ability to transform the abstract world of numbers into a tangible and exciting experience.
1. Rolling Towards Arithmetic Mastery: The Thrilling Adventure of “Roll and Add”
As we set forth on our journey into the heart of mathematical exploration, we unveil the exhilarating adventure known as “Roll and Add.” This interactive game combines competition, fortune, and the art of arithmetic. The ingredients are delightfully simple: a pair of dice and a blank canvas to record scores. Players take turns rolling the dice, then harness their arithmetic prowess to add the numbers unveiled by the dice. The victor of each round claims the crown with the highest sum and earns a cherished point. The ultimate laurel rests upon the brow of the one who accumulates a predetermined number of points, perhaps a regal total of 10. As players engage in this game, they not only sharpen their additional skills but also develop a keen sense of strategy as they decide when to push their luck and when to play it safe.
2. Target Number Challenge: Navigating the Expedition of “Target Number”
In the realm of numerical exploration, the “Target Number” expedition awaits. Players navigate the intricate pathways of strategic thinking armed with a steadfast target number – an enticing goal, such as 50. These mathematical explorers skillfully manipulate dice rolls to inch ever closer to the coveted goal. Imagine rolling a 4 and a 3 – a realm of numerical opportunities emerges: 43 or 34, each choice defining the trajectory. As the differences are scrutinised, and strategies are deftly woven, the victor emerges as the one with the most precise calculations, a mathematical maestro in the making.
3. The Symphony of Multiplication Bingo: A Melodic Melange of Math
In the enchanting symphony of “Multiplication Bingo,” multiplication transcends mere calculation and metamorphoses into a harmonious melody. The stage is set with Bingo cards adorned with a grid of numbers, each number born from the union of dice rolls and multiplication. Imagine rolling a 3 and a 5 – behold, the number 15 takes centre stage as the chosen melody. Players become virtuosos, rolling dice and marking off products on their Bingo cards. With each marked number, the symphony builds in intensity until the jubilant “Bingo!” announcement ushers in a mellow win.
4. The Epic Saga of Dice War: The Battle of Wits and Dice
The epic saga of “Dice War” transports players to a realm where chance and elementary arithmetic intermingle, birthing a battle of wits and dice. Warriors enter the arena, each bearing an equal number of dice – a brave five per participant. As the dice cascade, a battlefield of numbers is laid bare. The incantations of addition shape the contest, and the valiant warrior who commands the highest total emerges victorious, claiming a prized die from the defeated. This gripping narrative unfolds until a solitary figure stands triumphant, holding all the dice as tokens of their strategic conquest.
5. Unveiling Math Through Storytelling: Where Numbers and Narratives Converge
In the enchanting “Math Storytelling” odyssey, players become the weavers of a tapestry where words and numbers intertwine. This creative endeavour transports participants to a narrative ballet, where dice rolls contribute to the graceful choreography of a mathematical tale. Picture a beginning: “Once upon a time, there were 2 cats.” With a roll revealing a 4, the tale evolves, “They found 4 shiny coins.” This journey fosters not only additional skills but also nurtures the blossoming of language development and imaginative prowess.
6. Unravelling Dice Patterns: A Journey Through Patterns and Strategy
“Dice Patterns” beckons players to a labyrinth where patterns and strategy dance in harmony. Participants orchestrate sequences of numbers birthed from dice rolls, sequences that gracefully glide along the paths of addition or subtraction. A 2-4-6-8 sequence emerges with the roll of a 2, inviting the next player to carry the torch of the pattern. As patterns ripple through the gameplay and minds whirl with anticipation, complexity evolves, nurturing the growth of pattern recognition and strategic thinking.
7. The Thunderous Math Operations Race: A Sprint Through Mathematical Landscapes
The “Math Operations Race” propels players into a thunderous sprint across landscapes of arithmetic challenges. Here, players roll dice in quick succession, racing against time to conjure additions, subtractions, multiplications, or divisions that will lead them to a predetermined target number. A roll of 6 and 3 swiftly transforms into a victorious 9, edging the player closer to the threshold of triumph. When a person cracks the mathematical puzzle’s code, they triumph and yell, “Eureka!”
The symphony of maths dice games harmonises learning with joy, composing an opus where family bonds flourish and mathematical mastery blossoms. Amid the laughter and friendly competition, the seeds of mathematical enthusiasm take root, growing into an enduring love for learning.
Euroschool is your gateway to a world of educational excitement, where learning is beautifully blended with fun. At Euroschool, we understand the importance of engaging and interactive learning experiences. One delightful way to enhance mathematical skills while enjoying quality family time is through fun maths dice games played right at home. These games are not only a source of amusement but also provide a hands-on approach to mastering mathematical concepts. With the roll of the dice, children and parents alike embark on an adventure where numbers come alive, fostering a deeper understanding of arithmetic and strategy. As we encourage the spirit of curiosity and exploration, Euroschool invites you to discover the magic of maths through entertaining dice games that ignite a lifelong love for learning.


|Local Augmentation for Graph Neural Networks
|CC BY-SA - https://paperswithcode.com
Local Augmentation for Graph Neural Networks, or LA-GNN, is a data augmentation technique that enhances node features by its local subgraph structures. Specifically, it learns the conditional distribution of the connected neighbors’ representations given the representation of the central node, which has an analogy with the Skip-gram of word2vec model that predicts the probability of the context given the central word. After augmenting the neighborhood, we concat the initial and the generated feature matrix as input for GNNs.


My name is Onur Ucler and I currently work in a startup that builds CubeSat for NASA and Air-force as a senior software architect/senior research engineer. I am developing a reference firmware which complies with SOSA and VITA Tier-3 requirements. Previously, I was a co-founder of a startup named MyLearnMate. I developed a transformer model to generate video answers to math questions. I led a development team to build an iOS app, Azure API, and a website. As a side business, I develop trading algorithms for financial markets. I created a proprietary indicator that captures trends in the stock market with the help of Deep Learning algorithms. Most of the market tools that I developed are publicly available and integrated into Slack’s environment. Prior to startup experience, I worked at Intel Corporation for 8 years. My last position was a software architect prototyping/developing tools to validate power management capabilities and performance of Intel’s chipsets. Also, I had roles, as a lead system engineer for number of IP such as CSME, and PCIe, as design automation engineer, and a rtl design engineer for a number of products.
Some of the work done during my startup journey is highlighted here. Math video generation and stock trading tools are discussed here. For MyLearnMate, I and my co-founder intended to support students in math by providing them video explanations. We built a prototype for sample questions. Here is how it works:
Students enter a math equation:
x^2 + 2x + 1 = 0
Then the system generates an automatic video with voice. The video is generated for x^2 + 2x + 1 = 0 question given below.
Other question types supported by the system are listed:
- Linear equations: 3x + x = 12
- Linear 2d equations: x + y = 5, x + 2y = 5,x
- Quadratic equations: x^2 + 2x + 1 = 0
- Linear inequality equations: 2x + 5 < 0
- Radical equations: \\sqrt(x) = 5
The questions can be tested at https://mylearnmate.com/.
Based on my stock and option trading, I identified some of the challenges traders have then I developed those tools. First one is a scanning tool to determine the trend of stocks and that finds out what stocks to trade and when to enter/exit. The tool combines both fundamental and technical indicators and show the graphs of those stocks.
Slack API: trading-assistant runs daily after each trading day and send a report and video explanation as shown below.
Also, I developed an indicator called ExpInd which signals how strong the trend is. For instance, the general market might be in a bear market but if the ExpInd stays above its average and resists going down that is a strong signal for an uptrend.


Today on the Wake Up Call
What Supp with Mama G
A Different Kind of Christian
John Fisher has an interesting view of the true essence of the Christian using the Alcoholics Anonymous 12 Step program. Take a look.
Find a Celebrate Recovery program near you.
1.) What can you keep but cannot share and once you share it, you can’t keep it anymore?
2.) A number of children are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 18th child. How many children are there altogether? Hint: How many children are in half of the circle?
1.) A secret
2.) 22; in half of the circle there are 11 children because 18-7=11. Multiply 11×2=22!


How to Calculate the Date Nine Months From Today
Do you want to calculate the date nine months from today? If so, you’ll need a month calculator. These calculators are useful for calculating the date nine months in the future, and they also help you find out if the date you’re trying to calculate is possible. However, if you want to know how long it will take to reach a certain destination, you should first know how much you need to save for that journey.
Calculate 9 months from today
Do you want to know how many months from today it will be in the future? Well, you can use a months from today calculator to get the exact date. Simply type in the number of months, choose the direction of counting, and the starting date of today. Then click on the Calculate button. The result will be displayed in your current timezone. Once you know how many months from today it will be, you can plan your day accordingly.
If you were born nine months ago today, you would be born on Thursday 06 April 2023. This date is approximately three years from today. If you were born today, the date would be Thursday June 2022 at 11:35:28 PM (UTC). The same principle applies to the number of months from today. Then, you would have nine months to plan your day. The next step is to set a goal and make a list of goals for yourself.
Calculate 9 months from now
If you need to know the date nine months from today, you can use an online calculator. Simply input the quantity, nine, choose the period (months), direction (counting from) and start date (today) and click the Calculate button. You will be given the exact date in the specified timezone. Alternatively, you can calculate the number of days until the desired date. The result will be displayed in the format you specified.
If you want to know how long it will take you to reach the date nine months from today, you must know how much time you have left. For example, if you have a job interview on Tuesday, you can expect to meet that person on Tuesday. On the other hand, if you are looking for a partner, the date should be on or before Wednesday, March 09, 2023. Once you have your partner, you can proceed to the second step.


A thought occurred to me a couple of days ago. I was thinking about a number, and how that number fit into the knowledge base that I have in my head. As I thought about it, I then thought how there were other numbers that also fit into my knowledge base somewhere, somehow. I wondered how many such numbers there were, or if I could list even a few of them. So, here goes a sort of experiment to list some of the numbers that are in, have been in, or somehow have encountered my life, either in thought or experience.
55: The national speed limit put into place during the oil crisis from 1974 to 1995.
66. The number of books in the Bible (Protestant version).
4’ 8 ½”. The distance between the rails of a standard gauge railroad.
26,800,000,000. The known breadth of the universe, in light years.
3. Number of “persons” in the Godhead Trinity.
1. The loneliest number, according to Three Dog Night.
100. Highest denomination of circulating U.S. currency, in dollars.
13. Baker’s dozen.
5. The pink money in a Monopoly game, in dollars.
96. The age of my paternal grand dad when he died in 1966
3.14159 The (approximate, since pi is an irrational number) value of pi.
180. The sum of the angles of any triangle, in degrees.
10. The height of a basketball goal, in feet.
365 ¼ Approximate number of days in a calendar year.
666 A number frightening to many, but holds no special meaning for me.
256 My EMS radio call number in Harper County.
2,000 Number of pounds avoirdupois in a short ton.
Member of the set of imaginary numbers
50 Number of sprinkler heads on our small farm irrigation system when I was a youngster.
16 ½ Length of a rod in feet.
320 Number of rods in a mile.
(274,207,281 1) The largest known prime number (as of the beginning of 2017). It has over 22 million digits in it.
6 The number of my siblings plus myself.
4. The width of overturned dirt, in feet, that a 3-bottom plow will make in a field. Plowing a quarter-section of land with one three-bottom plow is a daunting and humbling experience.
2 The number of tools used in Euclidian geometry construction (compass and straight-edge).
2.71828 The number whose natural logarithm is 1 (aka the constant “e”). e, like pi, is an irrational number, so this is an approximation.
24 My age when I married. Best thing (almost) that ever happened to me.
776 My EMS radio call number in Harper County after the reorganization.
300,000,000 The speed at which my text message travels from my phone to the cellular point, in meters per second.
As you can readily see, numbers that may mean something to me may have no meaning for you. You may not have thought about imaginary numbers recently, or the speed of light, or even a baker’s dozen. But you do have numbers in your life, and numbers do mean something to you.
Take a little time and think of some numbers that have meaning for you and why they mean what they mean to you. It’s a pleasant exercise, and one that is sure to get you thinking past what’s for dinner tonight.


RRB GROUP D MODEL SET 12
(1)A train passes a 50 m long platform in 14 s and a man standing on a platform in 10 s. The speed of the train is
(a) 34 km/h
(b) 45 km/h
(c) 20 km/h
(d) 42 km/h
(2) The LCM of three different numbers is 120. Which of the following cannot be their HCF?
(3) A cooper rod of 1 cm diameter and 8 cm long is formed into a wire of uniform diameter, whose length is 18 m. The radius (in cm) of the wire is
(4) The equivalent single discount for two successive discounts of 15% and 10% is
(5) 18% of which number is equal to 12% of 75?
(6) The present ratio of the ages pf P and Q is 2 : 3 . If the age of P is 12 yr less than the age of Q, what is the present age of Q in years?
(7) If the area of a triangle with base 12 cm is equal to the area of a square with side 12 cm. The altitude of the triangle will be
(a) 24 cm
(b) 33 cm
(c) 16 cm
(d) 42 cm
(8) The system of patenting in India is
(a) System and Component Patent
(b) Product Patent
(c) Intellectual Property Right Patent
(d) Process Patent
(9) On papers, who declares war or peace?
(a) The Defence Minister
(b) The Parliament
(c) The President
(d) The Prime Minister
(10) Which of the following Ministries is not included in the Planning Commission?


Machine Learning Zoomcamp Update: Thursday, 9 September 2021
Date: 9 September 2021
Today, I completed the Sessions 1.6, 1.7 and 1.8.
Session 1.6 - Setting up the Environment
This session gave instructions on how to install any necessary software. Even though I don't use Conda, I already have all the necessary Python packages installed on my system. Still I am planning to do the homework tasks on Google Colab.
Session 1.7 - Introduction to NumPy
This session gave a refresher on basic NumPy methods. I completed this one quickly as I already knew everything he was talking about.
Session 1.8 - Linear Algebra Refresher
This session gave a refresher on Linear Algebra mainly Matrix algebra. Even though the topics covered were basic I really enjoyed this session.
- Vector operations
- Matrix multiplication and intuition behind it
- Identity Matrix
- Inverse of a Matrix
Estimated Time Taken: 1 hour


How To Calculate Attrition Rate In Research. Try applying this formula and calculate your. You can detect attrition bias by comparing participants who stay with participants who leave.
How to calculate attrition rate in research; Suppose a firm had 100. Fisk university men's basketball record;
The Result Is Your Attrition Rate In Decimal Form.
Finally, determine the number of employees who left. To calculate attrition you need to divide the number of e Human resources employees often use an attrition rate to determine the number of vacant or eliminated positions.
Calculating Attrition, Part 1 A Research Team Randomly Assigns.
Then, you need to know the number of new employees added that month. When data is collected at two or more points in time during an experiment, there will naturally be people who begin a study but then. Try applying this formula and calculate your.
Killing Of The Flower Moon Book Menu Toggle.
Calculate attrition rates and apply wwc standards for randomized. Attrition rate = # of employees that left / ((# of employees at the start of the year) + (# of employees at year. This is often called the mortality rate in market research circles.
Attrition Rates Are Values That Indicate The Participant Drop Out.
Customer attrition rate= 100/1000 = 0.1= 10%. Between attrition rates for the intervention group and. To calculate the annual attrition rate, here is the formula you will use:
Of Employees Attrition Rate = 20 / 310 Attrition Rate = 6.5% Therefore, The Firm's Attrition Rate For The Year 2018 Was 6.5%.
Fisk university men's basketball record; You can detect attrition bias by comparing participants who stay with participants who leave. So this business had a customer attrition rate of 10% by the end of the month.


is Associate Professor of Financial Mathematics at the University of Bologna. He is fellow of the Financial Econometrics Research Center, FERC, University of Warwick and Ente Einaudi, Bank of Italy, and member of the Scientific Committee of the Risk Management Education program of the Italian Banking Association (ABI). He has published in international journals in economics and finance, and he is co-author of the books Copula Methods in Finance
, John Wiley & Sons, 2004, and Structured Finance: The Object Oriented Approach
, John Wiley & Sons, 2007.
GIOVANNI DELLA LUNGA is a quantitative analyst at Prometeia Consulting. Prior to this he was head of Market Risk Methodologies at Prometeia and acted as Principal at Polyhedron Computational Finance, a Florence-based consulting company in mathematical models for financial firms and software companies. He also lectures at the University of Bologna in computational finance for undergraduates and runs courses in computational finance at the Bank of Italy. Giovanni is a member of the scientific committee of Abiformazione, the educational branch of the Italian Banking Association and manages the charge of screen-based educational program. His research background covers physics, chemistry and finance, and he co-authored Structured Finance: The Object Oriented Approach, John Wiley & Sons, 2007.
SABRINA MULINACCI is a Professor of Mathematical Methods for Economics and Finance at the University of Bologna, Italy. Prior to this Sabrina was Associate Professor of Mathematical Methods for Economics and Actuarial Sciences at the Catholic University of Milan. She has a PhD in Mathematics from the University of Pisa and has published a number of research papers in international journals in probability and mathematical finance.
PIETRO ROSSI is a Senior Financial Analyst within the Market Risk Group at Prometeira Consulting, specializing in the development of analytical tractable approximations for exotic options. Prior to this, he worked as senior scientist at ENEA in the high performance computing division and was also Director of the Parallel Computing Group at the Center for Advanced Studies, Research and Development in Sardinia (CRS4), working on high performance computing and large scale computational problems for companies such as FIAT. He has a PhD in physics from NYU and his scientific activity has been mainly in theoretical physics and computer science.
List of Symbols.
1 Fourier Pricing Methods.
1.2 A general representation of option prices.
1.3 The dynamics of asset prices.
1.4 A generalized function approach to Fourier pricing.
1.5 Hilbert transform.
1.6 Pricing via FFT.
1.7 Related literature.
2 The Dynamics of Asset Prices.
2.2 Efficient markets and Lévy processes.
2.3 Construction of Lévy markets.
2.4 Properties of Lévy processes.
3 Non-stationary Market Dynamics.
3.1 Non-stationary processes.
3.2 Time changes.
3.3 Simulation of Lévy processes.
4 Arbitrage-Free Pricing.
4.2 Equilibrium and arbitrage.
4.3 Arbitrage-free pricing.
4.5 Lévy martingale processes.
4.6 Lévy markets.
5 Generalized Functions.
5.2 The vector space of test functions.
5.4 The calculus of distributions.
5.5 Slow growth distributions.
5.6 Function convolution.
5.7 Distributional convolution.
5.8 The convolution of distributions in S.
6 The Fourier Transform.
6.2 The Fourier transformation of functions.
6.3 Fourier transform and option pricing.
6.4 Fourier transform for generalized functions.
6.6 Fourier option pricing with generalized functions.
7 Fourier Transforms at Work.
7.2 The Black–Scholes model.
7.3 Finite activity models.
7.4 Infinite activity models.
7.5 Stochastic volatility.
7.6 FFT at work.
A Elements of probability.
A.1 Elements of measure theory.
A.2 Elements of the theory of stochastic processes.
B Elements of Complex Analysis.
B.1 Complex numbers.
B.2 Functions of complex variables.
C Complex Integration.
C.2 The Cauchy–Goursat theorem.
C.3 Consequences of Cauchy's theorem.
C.4 Principal value.
C.5 Laurent series.
C.6 Complex residue.
C.7 Residue theorem.
C.8 Jordan's Lemma.
D Vector Spaces and Function Spaces.
D.2 Inner product space.
D.3 Topological vector spaces.
D.4 Functionals and dual space.
E The Fast Fourier Transform.
E.1 Discrete Fourier transform.
E.2 Fast Fourier transform.
F The Fractional Fourier Transform.
F.1 Circular matrix.
F.2 Toepliz matrix.
F.3 Some numerical results.
G Affine Models: The Path Integral Approach.
G.1 The problem.
G.2 Solution of the Riccati equations.


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What Is Function in Math – the Conspiracy
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Pi notation gives a compact means to represent many products. Linear Algebra is intended to fix problems of linear equations. Both of these places that appear to contradict one another are Math. However, you can say that mathematics isn’t your field and you’re not talented in solving mathematical difficulties.
Power Rule In actuality, the power rule is valid for any actual number n and therefore can be employed to differentiate an assortment of non-polynomial functions. Data Science is now a trending technology on earth today. So let’s look at a couple of examples. Example C it’s confusing to multiply at least two numbers at the same time. On occasion the problem has to be solved in steps. Look back at the issue and make certain that your answer is what was asked for.
The very first number in the multiplication is known as the multiplicand, the second number is known as the multiplier and the reply is known as the item. The function doesn’t need to be an equation. The algebra tutor portion of the program offers easy to comprehend explanations for each and every step of algebra problem solution. In math issues, the worth of x in a specific equation is frequently the question asked or the value to be solved.
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To recognize linear functions, you can produce a checklist of many items the function must meet. Variables are somewhat more flexible, simpler to read, and may give you more details. We’ve seen it is far better use a function table to spell out a function whenever there are a finite number of inputs for that function. Other functions have to make requests of the operating system in order to do their work. Demonstrate appropriate function notation.
The Rise of What Is Function in Math
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What You Should Do to Find Out About What Is Function in Math Before You’re Left Behind
To begin with, it’s helpful to provide a function a name. Operations within parentheses are complete first. We’ve seen it is far better use a function table to spell out a function whenever there are a finite number of inputs for that function. At first glance, it looks like a relation. That’s since it’s a one-to-one function.
What Everybody Dislikes About What Is Function in Math and Why
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In the event the people were working at precisely the same rate then we’d use the instead. This strategy is not really right, as there are billions of men and women in India and surveying each person is an excruciatingly hard job. We can observe it by taking a look at our two earlier examples. All that you want to do is to locate a trustworthy company that provides custom writing services.


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Nordisk Klang Clue
To solve you will need these elements
Examine the Scandinavian postcard closely, especially looking at the stickers - Do you notice anything?
Focus on the names on the postcard; they all contain Roman numerals. Your task is to decipher the number represented by each numeral in the names. Use the order indicated by the stickers (#1, an arrow, and a pointing finger) to arrange the Roman numerals.
Start by translating the Roman numerals in the names on the postcard. Then, follow the order indicated by the stickers: #1 leads to (IX)9, the pointing finger to (XVI)16, and the arrow (V)5. Finally, the last locker indicates (iV)4. Arrange these numbers in the given order, and you'll have the complete code: 91654.
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MIT OPEN COURSEWARE MASSACHUSETTS INSTITUTE OF TECHNOLOGY.MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. With more than 2,200 courses available, OCW is delivering on the promise of open sharing of knowledge.
KFUPM open courseware.The Department of Mathematics and Statistics is one of the largest departments of KFUPM with about 65 highly qualified faculty members in diverse areas of Mathematics and Statistics. Besides offering undergraduate and graduate programs in mathematics and statistics, it offers service courses to about 5,000 students per semester from various disciplines.
The California State University.Open CourseWare (OCW) are FREE online materials of entire courses (syllabus, presentations, assignments, and assessments) published by select universities.


Jun 21, 2022
In Business Forum
I shared the basic principles of ABtest before. Some friends asked: If I have not only two versions of AB, but three versions of Whatsapp Database ABC for testing, can I still use the ABtest method? Of course it works! It's just that the statistical method used is changed to: Whatsapp Database analysis of variance, and I will simply share it with you today. 1. The difference between multi-version and AB version If there are only two versions of AB to compare, then when doing hypothesis testing, the null hypothesis is: the mean/proportion of version A = the mean/proportion of version B. After that, as long as we can use the Whatsapp Database test results to overturn the null hypothesis, we can show that the AB versions have different means/proportions, and thus argue which version is better. The corresponding statistics are also designed accordingly. Whatsapp Database The problem becomes a little more complicated when there are multiple versions of ABCDE... . Because it is very likely that in this pile of versions, some have differences and some do not. If you test one by one, you have to compare n times, which is time-consuming and labor-intensive. How to complete the test efficiently? Second, the basic idea of multi-version testing A two-step method can be used. Step 1: Do an analysis of Whatsapp Database variance to test whether the means of these versions are equal. At this point, the original hypothesis is: A version = B version = C version = D version... In short, assume that they are all the Whatsapp Database same. If the assumption is not overturned, it means that everyone has the same mean, and there is no need to do the second step at all. If it can be overturned, then look at the gap between the two.


July 13 – 24, 2020 – Algebra I EOC Testing ONLY
Parents / Guardians and Students,
As you are aware, we are able to offer the Algebra I EOC during this upcoming testing window, to Nease students only. The exam is allowed to be taken on one day and will be administered in groups of nine students with one administrator, in accordance with current CDC guidelines. The exam consists of 2 x 90 minute sessions, a calculator is allowed in session 2 only. (TI-30Xa) Students testing in one day will be required to bring a lunch.
Students not opting for one day testing will attend on two consecutive days. Additionally, students should bring their own pencils, eraser and headphones (if they have the accommodation for this ).
Preparing for the Test
- Students may utilize Algebra Nation end of unit tests
- This can be found on the Student Links page of the school website
- sign in to math nation with your S number
- click on the link for Algebra Nation
Practice Test – Computer Based Test
- Follow the instructions on the FLVS guide to the computer based practice test.
- Practice Test
Practice Test – Paper Based (including answer key)
- Click on the link below to complete the paper based practice test from FSA Assessments
- Algebra I EOC PBT
Need more Help?
The following are review sessions which can be viewed via YouTube, courtesy of FLVS
- Part 1 – Equations and Inequalities, Linear and Exponential Functions, Systems of Equations
- Part 2 – Statistics, Polynomials, Factoring, Quadratics
Study daily for 20 minutes per session, work through the questions and show your working out. We look forward to seeing you in July.
You can always use Google to search for more practice tests, click the link to take you there.


Today is Friday the 13th, the day when more accidents happen because Paraskevidekatriaphobics are concerned about accidents. Or is it the day when less accidents take place, because people stay home to avoid accidents? Not altogether clear, it seems.
Whether safe or dangerous, how often do these Friday the 13th take place, exactly? Are there years without it, or with more than one? That’s a question which should have a clearer answer. Let’s try to figure out the probability to observe N such days in a year picked at random.
First, note that if you knew what the first day of that year was, you could easily verify if the 13th day for each month was indeed a Friday. Would that be sufficient? Not quite – you would also need to know whether the year was a leap year, these years which happen every 4 years and have an extra day, February the 29th.
Imagine that this year started a Monday. What would next year start with? If we are in a regular year, 365 days = 52 x 7 + 1; in other words, 52 weeks will elapse, the last day of the year will also be a Monday, and next year will start a Tuesday. If this is a leap year, next year will start on a Wednesday.
Why do I care? Because now we can show that every 28 years, the same cycle of Friday the 13th will take place again. Every four consecutive years, the start day shifts by 5 positions (3 “regular” years and one leap year), and because 5 and 7 have no common denominator, after 7 4-year periods, we will be back to starting an identical 28-years cycle, where each day of the week will appear 4 times as first day of the year.
Now we now that any 28 years cycle is a complete cycle. We just need to pick any year to start with, and enumerate through sheer brute-force over 28 years days that fall on the 13th day of the month, and are a Friday. Let’s do that with a quick-and-dirty C# console app:
var startYear = 2000;
var cycle = 28;
for (int year = startYear; year < startYear + cycle; year++)
for (int month = 1; month <= 12; month++)
var candidate = new DateTime(year, month, 13);
if (candidate.DayOfWeek == DayOfWeek.Friday)
Running this yields the following result:
- There is always a Friday the 13th. ALWAYS.
- There can be as many as 3 occurrences in a single year.
Here is the full distribution:
|# of Friday the 13th
||# of Years
I must say I was a bit surprised to see so many occurrences; because of the mystique around that date, I expected it to be a bit of a rare event.
In any case, whether you stayed home today or ventured out, I wish you all a safe and lucky Friday the 13th!


3-4-3-4-cup-equals, this equals 1.5 cups. the 'cup' is a measurement that measures volume. it is customary and is generally used in cooking to measure liquids. hence, it's often considered a fluid measurement.. If you double 3/4 of a cup, you'll get 6/4 cups, which can be simplified as 3/2 cups or 1 1/2 cups. in decimals, 3/4 of a cup is .75 cups, and .75 doubled is 1.5 cups. since a united states customary..., 3 4 cup equals how many liters. 1 ml 4 tablespoons, 1/4 cup, 2 ounces, grams. 5 1/3 term, abbreviation, nationality, dry or liquid, metric equivalent, equivalent in .... There are officially 8 fluid ounces to a standard cup answer :- 3/4 cup holds 6 fluid ounces of volume or space., 6 six ounces..
4 cups = 1000 mls = 32 fluid ounces = i quart = 1 kg water a better solution is to buy a kitchen scale as the above comparisons are approximations and do not work for materials like flour, chopped ..., there are 4 tablespoons in 1/4 of a cup so there would be 12 t in 3/4 cups. 0 5 0. log in to reply to the answers post. I'm using a recipe that calls for 3/4 pints heavy cream but my measuring cup only goes by cups so what is the conversation?, 1 us cup = 16 us tablespoons 3/4 us cup = 12 us tablespoons 34 tbsp = 2.12 cups 1 cup = 16 tablespoons 1 tablespoon = 0.06 cup


Math Skills Builder aims to reinforce the learning of basic concepts in Math such as shapes and colors, counting numbers and representations, addition and subtraction among others. The activities are meant to captivate the learner's interest and eventually engage them to activities that will not only deepen their knowledge but will stir and develop their critical and creative minds.
The Skills Builder Series is a helpful tool in letting young learners practice their skills in five subject areas: Reading, Writing, Math, Filipino, and Art. Specifically designed for home learning, all books offer fun enrichment activities and performance trackers for parents/educators.
Rowena V. Dagdag and Aileen O. Ruivivar
8.25 x 10.75in
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For orders in Balance Luzon, Visayas & Mindanao, items will be shipped via GoGo Xpress or LBC.
For items under pre-order, do expect delivery in about 1-2 weeks time.
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CONFERENCES and WORKSHOPS:
Spectral Days 2017, Stuttgart, Germany, April 3-7, 2017.
SUMA 2016: Primer encuentro conjunto de la Sociedad de Matemática de Chile y de la Unión Matemática Argentina, Valparaíso, Chile, 14-17 de Diciembre de 2016.
Shape Optimization and Isoperimetric and Functional Inequalities, CIRM, Luminy, France, November 21-25 (2016)
QMath13: Mathematical Results in Quantum Physics, Georgia Tech, Atlanta, GA, US, October 8-11, 2016.
Saint Petersburg Conference in Spectral Theory, dedicated to the memory
of M. Sh. Birman, Euler Institute, Saint Petersburg, Russia, July 3-6,
Spectral Geometry Conference: 50 Years of Hearing Drums. Spectral Geometry and the Legacy of Mark Kac. Santiago de Chile, May 16-20, 2016.
International Congress of Mathematical Physics (2015), Santiago de Chile, August 3-8, 2015.
Shape Optimization and Spectral Problems, ICMS, Edinburgh, June 29-July 3, 2015.
Laplacian and Heat Kernels: Theory and Applications, BIRS, Banff, Canada, March 22-27, 2015.
X Americas Conference on Differential Equations, Buenos Aires, Argentina, February 16-20, 2015.
Spectral Days 2014, CIRM, Luminy, France, June 9-13, 2014.
Mathematical Congress of the Americas 2013, Guanajuato, México, August 5-9, 2013; Special Session on Mathematical Physics.
Spectral Theory of Laplace and Schroedinger Operators, BIRS, Banff, Canada, July 28-August 2, 2013.
The 6th Pacific RIM Conference on Mathematics 2013, Sapporo, Japan, July 1-5, 2013 [Spectral and Scattering Theory Session].
Thematic Trimester at Institut Henri Poincaré:"Variational and Spectral Methods in Quantum Mechanics", Paris, Spring 2013.
Hamiltonian in Magnetic Fields (Special Semester at the Mittag-Leffler Institute, Sweden, September 3-December 15, 2012).
International Congress of Mathematical Physics, ICMP 2012, Aalborg, Denmark, August 6-11, 2012.
[Special Session on "Quantum mechanics and spectral theory"]
Elliott Lieb Conference: "Mathematical Physics of Many Particle Systems", Berlin, July 12-14, 2012.
Workshop on Geometry of Eigenvalues and Eigenfunctions, CRM, Montreal, June 4-8, 2012.
Shape optimization problems and spectral theory, CIRM, Luminy, Marseille, May 28-June 1st., 2012.
Spectral Days 2012, Münich, Germany, April 10-13 2012.
MOPNET, EPSRC Matrix and Operator Pencil Network, Meeting 6, Bath, England, April 2-3 (2012).
Summer School on current topics in Mathematical Physics, ESI, Vienna, August 16-24, 2011.
First AMS-Sociedad Matemática de Chile, Pucón, Chile, December 15-18, 2010.
Spectral Days 2010, Universidad Católica, Santiago, Chile, September 20-24, 2010.
International Conference on the Isoperimetric Problem of Queen Dido and its Mathematical Ramifications, Carthage, Tunisia, May 24-29, 2010.
Selected Topics in Spectral Theory (Program), ESI, Vienna, May 5-July 25, 2009.
Analysis and Probability in Quantum Physics, PASI 2006, Universidad Católica, Santiago, Chile, July 24-August 4, 2006.
Low Eigenvalues of Laplace and Schrödinger Operators, American Institute of Mathematics, Palo Alto, California, May 22-26, 2006.
Relativistic Quantum Coulomb Systems, Santiago de Chile, August
(Sept 25, 2016).