What is STEM?
STEM stands for Science, Technology, Engineering, and Mathematics. These subjects are often taught separately, but are all interconnected just as reading, writing, and speaking are; understanding in each of the STEM fields deepens understanding in the others.
Science includes biology, chemistry, archaeology, physics, psychology, and any other subject which interprets the world through a logical lens.
Technology includes the use or investigation of any device used to make, learn, or do something.
Engineering, less taught in primary school but increasing in popularity, includes mechanical studies, chemical tinkering, aeronautics, or any other method by way innovation is tested systematically.
Mathematics is the way by which the world is studied through numbers and logic.
Why STEM Mentoring?
Three main strategies drive our reasoning behind STEM Mentoring.


I recently wrote a two-part series about the famous mathematical constant/artistic proportion known as the Golden Ratio, so I decided to compile a list of all the studies I could find published online about the aesthetics of the ratio: a "master list" of sorts of what people have proven about it scientifically. For background on what the golden ratio is and where it's found in math, read Part 1 of my series, and for a breakdown of some of the legends around it, check out Part 2.
Disclaimer: This list is by no means exhaustive! However, I included almost every study I encountered researching my golden ratio blog posts, including every one that was referenced by another online news article, as well as others that I found particularly interesting or high-quality. Without further ado...
This 1995 paper is easily the most robust and compelling document I've found on the golden ratio. It painstakingly compiles nearly every the empiric studies about the aesthetics of the golden ratio from the mid-19th century to the early 1990s. (The introduction is also an excellent account of the ratio's history.) I wouldn't recommend reading the 30+ page behemoth yourself; to spoil the ending, the author's personal opinion is that the evidence points toward at least some measure of preference for the golden ratio—but a very fragile one.
This study, first published in 2009, used manipulated photos to test the attractiveness of various length and width proportions in the female face. After studying the preferences of 126 university students across four experiments, they found attractiveness to be optimal "when the face’s vertical distance between the eyes and the mouth is approximately 36% of its length, and the horizontal distance between the eyes is approximately 46% of the face’s width." These proportions match the average human face.
This 2009 paper uses math and logic to argue that one's eyes will scan a rectangle most quickly when it has a length to width ratio of around 3:2. The author then argues that, because the golden ratio is so close to a 3:2 proportion, this conclusion explains why golden rectangles are so visually pleasing, or "‘breathe’ and ‘flow’ better than most other shapes," as the author puts it.
This one's filled with science jargon and concepts I have no knowledge of, although I could discern enough of the details to summarize it. Essentially, this 2015 scientific study examined the neural responses of 30 participants across 4 experiments when confronted with abstract images of various proportions. The researchers found that patterns that contained golden ratio proportions took longer for participants to visually process. They theorized that this increased length of processing time might account for the golden ratio's perceived value in art, i.e., "I've been looking at this artwork for slightly longer than usual, it must be significant!"
In this 2008 study, 36 participants used a 10-point scale to rate faces from an extensive image database. The researchers used a graphic user interface to analyze the proportions of the images (based on facial landmarks, like the inner corners of the eyes). Of the proportions tested, they found that facial attractiveness was correlated with 5 out of 6 "neoclassical canons," 3 out of 11 symmetries, and 6 out of 17 golden ratios.
This study, published in 2015, is particularly unusual both because it took place in Taiwan, rather than the western world, and because it questioned whether personality type was related to proportion preferences. 120 participants had their Myers-Briggs personality types tested and then rated each of 30 rectangles on a 1-5 scale. They found that squares were the most preferred shape, while there was moderate preference for the golden ratio, and ratios longer than the golden ratio tended to be disliked. And yes, rectangle preference varied with personality type; it also varied between males and females.
To stay up-to-date on M•A•D Symmetry and learn some weird facts to impress your friends with, use the sign-up form below!


We provide leadership within NIST in the application of applied and computational mathematics to the solution to science and engineering problems arising in measurement science and related applications. This is accomplished via a program of R&D in mathematical and computational techniques and tools, collaboration with NIST and external scientists, and the dissemination of reference data and software.
The ITL Mathematical and Computational Sciences Division was renamed Applied and Computational Mathematics on June 20, 2010
Details of technical activities of the Division are provided in our Yearly Reports: 2013 , 2012 , 2011 , 2010 , 2009 , 2008 , 2007 ,2006 , 2005 , 2004 , 2003 , 2002 , 2001 , 2000 .
You are invited to attend our Division Seminar Series .


Use the link below to find out how children at KMA progress through maths from EYFS to Year 6
In Mathematics, like all other subjects, we recognise the importance of the methods and practice of teaching (the pedagogy) we choose to use in enabling pupils to know more, understand more and remember more. In Mathematics, the following approaches will be used, and be evident in pupil discussion, observations and work in books, in order to ensure that the learning opportunities and skill development are as effective as possible and that pupils progress throughout the year and across year groups during their maths experiences in school:
At King’s Meadow Academy we follow the White Rose scheme of work to support our children in their mathematical development.
On 7th May we will be supporting the NSPCC to raise funds through Number Day!


2 edition of Proceedings of the 14th Conference of International Linear Algebra Society found in the catalog.
Proceedings of the 14th Conference of International Linear Algebra Society
International Linear Algebra Society. Conference
Includes bibliographical references and index.
|Statement||edited by Er-Xiong Jiang, ChuanQing Gu, Ying-Hong Xu.|
|Contributions||Jiang, Erxiong., Gu, ChuanQing., Xu, Ying-Hong.|
|LC Classifications||QA184.2 .I58 2007|
|The Physical Object|
|Pagination||v, 481 p. ; :|
|Number of Pages||481|
|LC Control Number||2009437368|
Proceedings of the IEEE International Conference on Computer Vision, pp. (ICCV oral presentation) Proceedings of the 14th International Conference on Interaction Design and Children. pp (IDC ) Numerical Linear Algebra. (pp.) Society for Industrial and Applied Mathematics. (). Proceedings of the 15th International Conference on Numerical Analysis and Applied Mathematics, ICNAAM , September, The MET Hotel, Thessaloniki, Greece. DOI: / Célia Nunes, Anacleto Mário, Dário Ferreira, Sandra S. Ferreira and João T. Mexia.
Conferences in General Algebra and Related Fields. 57th Summer School on General Algebra and Ordered Sets, Hotel Cingov, Smizany, Slovakia, August September 5, AAA, The th Workshop on General Algebra, Johannes Kepler University Linz, Austria, June , AAA99, The 99th Workshop on General Algebra, University of Siena, Italy, February 21 . Linear algebra is an important area of mathematics and it is at the heart of many scientific, engineering, and industrial applications. Research and development in linear algebra include theoretical studies, algorithmic designs and implementations on advanced computer architectures, and applications to various disciplines.
History of IWOTA First IWOTA Meeting. The International Workshop on Operator Theory and its Applications was started on August 1, , adjacent to the International Symposium on Mathematical Theory of Networks and Systems (MTNS) with goal of exposing operator theorists, even pure theorists, to recent developments in engineering (especially H-infinity methods in control theory) which had a. Society for Industrial and Applied Mathematics International Linear Algebra Society Heinrich-Heine-Universitat Du¨sseldorf Bergische Universitat Wuppertal Gesellschaft von Freunden und Forderern der Heinrich-Heine-Universitat Du¨sseldorf Gesellschaft der Freunde der Bergischen Universitat The MathWorks Cadac GmbH.
Present day economies in cataloging
Master the AP English Literature & Composition, 1st edition (Master the Ap English Literature & Composition Test)
Developments in modern painting materials
Photography, source and resource
Oscillation of piles in marine structures - a résumé of the full-scale work carried out at Immingham
[Interrogatories vpon which ... churchwardens shalbe charged, for searche, of al such things as now be amysse.]
Norwegian church in its international setting
Proceedings of The 14th Conference of International Linear Algebra Society. This volume contains selected papers presented at the 14th Conference of the International Linear Algebra Society (ILAS), which was held in Shanghai (China) during JulyThe main objective of this mathematical conference on linear algebra and its applications is to encourage research and interaction of researchers interested in all aspects of linear algebra.
About the Conference. This is the meeting of the SIAM Activity Group on Linear Algebra. The 23rd Conference of the International Linear Algebra Society (ILAS ) is embedded in LA Linear algebra is an important area of mathematics and it is at the heart of many scientific, engineering, and industrial applications.
Skopal T, Bartoš T and Lokoč J On (not) indexing quadratic form distance by metric access methods Proceedings of the 14th International Conference on Extending Database Technology, () Liu Y, Ning P and Reiter M () False data injection attacks against state estimation in electric power grids, ACM Transactions on Information and.
International Conference on Linear Algebra and its Applications (ICLAA ) 19, This conference has been endorsed by the International Linear Algebra Society.
Register Download Brochure Abstract Template. Purpose. Other articles within the scope of ICLAA and IWMS may be submitted to the proceedings of ICLAA /IWMS RW- th International Conference on Internet Technologies and Society ICITS is a prestigious event organized with a motivation to provide an excellent international platform for the academicians, researchers, engineers, industrial participants and budding students around the world to SHARE their research findings with the global experts.
Linear Algebra Related Conferences. ILAS Homepage ; ILAS Publications ; ILAS - NET; Linear Algebra Education; Linear Algebra Journals. Special Issue on the 11th Conference of the International Linear Algebra Society, Coimbra, 11th Conference of the International Linear Algebra Society, Coimbra, (Coimbra ) July • University of Coimbra, Coimbra, Portugal.
The 20 th ILAS Conference in Leuven. In the 20 th Conference of the International Linear Algebra Society will take place in the center of Leuven, Belgium, at the KU Leuven, which has a tradition dating back to We are looking forward to welcome you in Leuven for ILASenjoy the conference and we hope you will reserve some time to look around.
The IMA is pleased to announce the Seventh Biennial IMA Conference on Numerical Linear Algebra and Optimization. The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra.
The conference is the third meeting within prof. Le Donne's ERC project GeoMeG (Geometry of Metric Groups). The idea for the meeting is to focus on the following subjects: 1) large-scale geometry of nilpotent groups (and as the sub-Riemannian geometry appear as asymptotic cone) 2) Heintze groups (= homogeneous negatively curved manifolds) and their boundaries (which are nilpotent groups.
The Bulletin of the International Linear Algebra Society IMAGE Serving the International Linear Algebra Community Issue Num pp.Fall Editor-in-Chief: Jane M.
Day, Dept. of Mathematics, San Jose State University, San Jose, CA, USA ; [email protected] The conference proceedings will appear as a special issue of.
Fourteenth International Conference on Numerical Combustion (NC13) International Linear Algebra Society Meeting (ILAS ) & Jobs Conferences Customer Service Digital Library Fellows Program History Project Journals Membership Prizes & Recognitions Proceedings Public Awareness Reports Sections SIAM News Students.
Proceedings of the ninth conference of the International Linear Algebra Society (ILAS), Haifa, Israel, June 25–29, Article in Linear Algebra and its Applications March with 14 Reads. by Sven Hammarling, Nick Higham and Françoise TisseurThe conference Advances in Numerical Linear Algebra: Celebrating the Centenary of the Birth of James H.
Wilkinson, took place at the University of Manchester, MayThe purpose of the conference was to discuss recent developments and future challenges in numerical linear algebra and to celebrate the. In cooperation with the International Linear Algebra Society. The Conference will be held in the University Center Building 86 on THIS MAP.
Online Conference Proceedings. Are now available HERE!. About the Conference. The Eighth SIAM Conference on Applied Linear Algebra is the latest in a successful series of meetings that began in Raleigh.
Preface to the 17th ILAS Conference ‘Pure and Applied Linear Algebra: The New Generation’ Proceedings, Braunschweig, Germany, Matthias Bollhöfer. Euro-Par ' Proceedings of the 14th international Euro-Par conference on Parallel Processing Solving Dense Linear Systems on Graphics Processors Pages – The proceedings of the conference can be found in volumes of Linear Algebra and its Applications.
ILAS conferences were held the next 4 years, alternating between the United States and Europe, before beginning the standard pattern of holding. Linear Algebra Conferences is for the researchers, scientists, scholars, engineers, academic, scientific and university practitioners to present research activities that might want to attend events, meetings, seminars, congresses, workshops, summit, and symposiums.
Proceedings of the eighth conference of the International Linear Algebra Society (ILAS), Barcelona, Spain, July 19–22, Article in Linear Algebra and its Applications (1) August. The generalized inverses of the rectangular Vandermonde matrix, Proceedings of the 16th Conference of the International Linear Algebra Society (ILAS), 21 – 25, Pisa, Italy.
(after invitation to the mini-symposium “ Generalized Inverses and Applications ” (Nieves Castro-Gonzalez, Pedro Patricio)) (with Kalogeropoulos G.I. and Karageorgos A.As per available reports about 89 journals, 86 open access articles 10 Conferences, 30 workshops 13 National symposiums are presently dedicated exclusively to Algebra.
Algebra is one of the broad parts of mathematics which has number theory, geometry and analysis. Algebra is the study of symbols and the rules for manipulating symbol and is a unifying line of all of mathematics.vector spaces, linear maps, determinants, and eigenvalues and eigenvectors.
Another standard is book’s audience: sophomores or juniors, usually with a background of at least one semester of calculus.


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Joyce Tan Teng
My child has been failing Maths during his primary school days. He started to attend coaching by teacher Andy of Learning Voyage in Secondary Maths after he went to Sec One. He is going Sec 3 next yr. I am grateful to Teacher Andy’s coaching. My child has improved in his Maths, from failing to passing Maths ! Good passes ! We can see the progression in my child’s Maths. 👍. Thank you teacher Andy, Thank you Learning Voyage! We are thankful we found you.
Alwyn Lee Mei Leng
Two of my friends recommended Teacher Andy to me because for their daughters, Maths is their weakest subjects in school but after attending Teacher Andy's classes they achieved distinction in Maths. So I sent my 2 children to Learning Voyage. Andy is a very patient teacher. He helps my children to build good foundation and develop their mathematical abilities. He motivates my children to always try their best and makes Maths interesting for them. My daughter scored distinction for her Maths and Add Maths in the O Level Exam last year. Because of his dedication, patient and commitment to students' success, I have recommended Teacher Andy to many of my friends. Andy, thank you for being a great Maths teacher and making a difference in my children's lives. May you continue to inspire greatness in all of your students.
My daughter, Joscelin join Andy's tuition class since secondary two. Since then, her grades have improved tremendously these past three years and she eventually scored A1 for both maths. As a tutor, Andy is dedicated, helpful and caring and I'm greatly appreciative of his help in coaching my daughter. Keep up the good work, Andy!
J Tai Goh
My son Xavier has been with teacher Andy for 4 years. I can really see his progress from a weak in mathematics student to a fundamentally strong and can grasp complex concepts. His patient approach not only improve my son mathematics grade to both A1 in O level, it has also build up his confidence that he can help other weaker students. We truly appreciate Andy's guidance and help. He's more than a good teacher, he's really a fantastic mentor to my son. Thank you teacher Andy!
Xavier Goh Hl
Teacher Andy has taught me mathematics for 4 years. Throughout these 4 years, I can safely say that teacher andy is the most patient teacher I ever had. He has never ever lost his temper at his students and will keep reteaching the concepts of math until his students fully understand no matter how tiring and troublesome it is. The way he teaches math is very clear. This has allowed me to grasp the concepts much easier,and under his care his guidance, it allowed me to score distinction in both Elementary and Additional Mathematics.
I had many Math tutors before deciding to join Learning Voyage and none of them could compare to Mr Woo. After trying out private tuition and numerous Math tuition centres such as Mavis, I am glad to say that among all of them, Learning Voyage has definitely helped me in my grades. I entered with an extremely weak foundation in Math and came out with A1s for both Maths during Olevels. The notes and practices given out during classes are always of great standard and lessons are always engaging! A group tuition may seem intimidating at first but I can assure you that it is a very conducive study environment and lessons are tailored for each student needs. I highly recommend Learning Voyage as I am sure that my results would not have been possible without the dedication and encouragement I recieved.
Ang Kai Jie
The teacher, Andy, is great, caring, patient, passionate and always made sure we understood what is being thought. He shares many life stories and also, does not hesitate to provide us with different math methods to solve a question. At times, when we are really exhausted, he will give us a question relating to our real life application and i got to learn more stuff. He goes the extra mile and made sure we were well prepared for our o level. He even made a box containing things inside to spur us on for the “marathon” Overall, it is highly recommended and he is the best math tutor you can ever find, sign up now!!!!��
Hui Ru Chia
Mr Andy is very patient and aid me a lot for my Amath.I remember coming in with F9 for amath. He help me a lot, giving me tips and helping me solve difficult questions. He is a great teacher.👍🏻 THANK YOU!!
Heartfelt thanks to Mr Woo..😍👍🏼 My son joined Learning Voyage 6 weeks prior to his SA2.. he is a hardworking boy, spend many many hours in maths practices, he will do & do & file all his corrections & make sure he doesn’t make mistakes again. His time is all revolved in only Maths.. but sadly his result is never matchable to the time & effort he put in... it’s quite a heartache for him & the parents.. But WOW! WOW! WOW.. his maths had scored a 80.5/100 for this SA2. When we signed him up, we never expect a miracle at all.. just only want him to get the concept right.. but his result was excellent.. we really are overjoyed & just need to share this joy.. bragging away... haaa MR WOO, many thumbs up ..👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼
Xin Yi Lam
was failing my Amath really badly in sec 3 but was recommended by my friends to join his tuition centre and i started to understand more and more topics after joining his tuition. this is because he is very understanding and patient. mr woo would use different ways to encourage and motivate his students to not give up. not only during tuition, he would clarify and help me to understand more through whatsapp. thanks to him, i am really satisfied with both my emath and amath olvl results!! 🙂 would recommend learning voyage to my juniors, family and friends. thank you mr woo!!
Joined in secondary 4 and thought it was too late to save my grades for math because i was constantly either failing or boarderline passing. However, Mr Andy's teaching made both math and amath fun. His constant encouragement is the main reason why I am able to improve my grades exams after exams and eventually obtaining a distinction in my O'levels. Mr Andy teaches math topic by topic making it easier for me to spot the topics i am weak in. To Mr Andy: Thank you for always encouraging me and believing in me!! I've improved tremendously and I can't thank you enough for the effort you have put in the ensure that I do well for the 2 maths �
Thanks Mr Woo for teaching me since secondary 2 and for making math lessons fun for me and teaching me to enjoy the subject more and more throughout the years.
I first enrolled in Learning Voyage at Secondary 1 as I’ve been failing math since primary school. The failure has made me disliked the subject the most. Although it’s a group tuition, Mr. Andy caters to the needs of every student in the class. A year before my national exams, I got a private home tutor as I thought it would be more beneficial for me. However, I found myself going back to Learning Voyage a month after. During the lesson, if any one of us encounter a complicated question, Mr. Andy will discuss it with the class. This has made us more flexible when answering questions. In addition, we are more exposed to various question types. With Mr. Andy’s guidance, I got a grade 2 in my N(A) Levels. Not only did he guide me, he motivated me and made sure I did every practice to the best of my ability.
Mr Woo is a dedicated tutor who constantly checks on the progress of his student and tries his best to make them understand the concepts. Although classes are conducted in groups, the class size is small so that students are able to clarify their doubts immediately. Thanks for guiding me throughout the 'O' Level period, Mr Woo!
My daughter has been failing her math since Sec one, after trying with other Tution centers, she is unable to handle her math, but after I send her to Learning Voyage during her last year of Sec study, not only did she pass but also scored A for her math. I would like to thank Andy, thank you so much!
I first joined Learning Voyage as my algebra was very weak at secondary two. I could not understand the rules of algebra but Mr Andy took the time and effort to teach me. Right after strongly understanding algebra, my mathematics significantly improved throughtout the years! With his patience to teach and the effectiveness of his lessons, nothing could go wrong. Thank you Mr Andy for teaching me throughout the years, I am very grateful to have you as my tuition teacher!
Tan Suan Leng
Back when I was still a secondary one student, my Math was really weak. However, ever since I joined Learning Voyage, my math result has significantly improved under the help of Mr Andy. Not only was his explanation of mathematical concepts clear and precise, but it was also easy to understand. Mr Andy is an amazing and innovative tutor and all of his lessons are a pleasant experience for me. Thank you Mr Andy for your guidance in Math.
my math results were always terrible and i can never pass math ever since sec 1 . after joining this tuition , i notice my math results starting to improve and now that i've graduated from sec 4 , i'm veryyyy please with my results .
My math grades was always at the borderline, not being able to understand the topics and the lack of practice. After signing up Learning Voyage under Mr Andy for almost 2 years. My grades have greatly improved and I am able to score a distinction for maths! (A1 / A2). Mr Andy has help me improve my math by making sure that I know every topic for exam. In addition, he also makes us practice more on topics we are weaker at, making sure that there is no doubts for every topic learned. His classes are enjoyable and motivating, also he makes lessons interesting, which made my math as my forte - strongest subject compared to the rest of my subjects. Lastly, during exam periods, he provided extra lessons for students, so that we could be well prepared for the test. He is an amazing tutor! And if anyone one who is looking for math tutor please find him! It was the best tuition I had so far compared to many others. Thank you for all the effort and hard work you done for me Mr Andy!
Andy is an awesome tutor to me as he is always very encouraging and patient. Also wlling to go the extra mine to explain something that I did not fully understand. He always made lessons enjoyable and lively instead of how other tutors may teach, all work and no play. Making me have a greater interest in math and keen on learning more. Thanks again teacher Andy as I would not have been able to get both my maths(especially Amath) to both grade As!
Thanks for teaching me! My grades improved alot thanks to your fun and engaging lessons! 😀
Hi Mr Andy! Thank you so much (really) for tutoring me 🙂 I’m the type that cannot pay attention in class especially if the lessons are monotonous. Hence as you can tell, I didn’t focus during maths class in sec 1 (it was so bad I tell you). Since I wasn’t paying attention during class time, my maths grades have always been either a fail or just pass. However when I started tuition under Mr Andy, my grades has improved A LOT. A few reasons are because his lessons are interactive, he goes through the syllabus thoroughly, BUT the main reason is because he is very encouraging. (ง •̀_•́)ง Mr Andy has been pushing me and encouraging me each time as I attend his tuition. Whenever I make a mistake in doing the questions (and it’s mostly careless haha), his first reaction is: “aiyoooooh Junnnnnnn” and he would stare at me something like => щ(ಠ益ಠщ), but he never fails to say: “jiayou Jun you can do it!” and does this action => (ง •̀_•́)ง Although these are just simple gestures that he does often and that you might not realize but this shows his encouragement for his students that he wants them to do their best, and his dedication to be there and guide us 😀 So yes please do be tutored under mr Andy if you ever need help! These reviews are written personally by us, his ex students. To Mr Andy: Thank you for encouraging me to do my best and for believing and not giving up on me to reach my full potential! I wish you all the best 🙂 And yes distinctions for both E and A maths (ﾉﾟ▽ﾟ)ﾉ
I have had quite a few tutors in the past, but none of them were as cool as Andy. Not only could he teach well, but he could also connect with us students. I could talk to him about all sorts of things, whether it be about my school life or even football (he is a Man Utd fan). But of course, he knows when to be serious as well. This balance makes his lessons far more enjoyable and conducive than other tutors, which allows me to absorb much more. I would eagerly await each of Andy’s lessons, whereby I would normally despise other tuition. As a mathematics tuitor, Andy is objectively brilliant. His math skills are god-tier; he could solve math questions that even rendered my school teachers helpless. He could even forge simpler yet more effective methods to questions, rather than the convoluted solutions that the school provides. He is also extremely patient, and will not give up until students truly understand. I used to be a plebeain before i was taken under Andy’s tutelage. But now, I a mathematics patrician, and a proud owner of distinctions for my ‘O’ Level mathematics examinations. Truly, Andy is a wonderful tutor. 10/10 would tuition again
Roses Are Red Violets Are Blue Tuition Is Cool With Andy Woo! Andy is not only an amazing tutor, he can also be an amazing friend. He not only guided me through my difficulties with mathematics, he also guided me through the O Levels by providing support and encouragement that no other tutor can provide. He is a very friendly, funny ,and open person, who you will feel comfortable around. All in all i have achieved success after joining Learning Voyage and i have no regrets with choosing Andy’s tuition. TLDR: 0As>2As in maths


The interpolation principle of numerical control lathe, rounding
Interpolation principle of numerical control lathe, a release date: 2015 - 06 - 18 clicks: 3034 times in the actual processing, CNC lathe processed workpiece contour shapes, strictly speaking, in order to meet the accuracy requirement of the geometry size, cutting tool center path should be accurately according to the outline shape of workpiece to generate, for simple curve nc system can be relatively easy to implement, but for more complex shapes, if direct generation can make algorithm becomes very complex, computer work also correspondingly increases greatly, therefore, in practical application, often with a short straight line or arc fitting can meet the precision requirement ( Also has the need to parabola and the situation of the high order curve fitting) The fitting method is & other; Interpolation & throughout; , essentially the process of data interpolation is close. CNC lathe interpolation task is according to the requirement of the feed rate, starting point and end point in the contour coordinates to calculate the number of intermediate point between, time needed for each intermediate point calculation directly affect the speed of system control, and the calculation precision of interpolation point coordinate values among and affect the control precision of the numerical control system, therefore, interpolation algorithm is the core of the numerical control system. Interpolation algorithm, after decades of development matures, a lot of more phyletic. Generally speaking, from the mathematical model, mainly has linear interpolation and quadratic curve interpolation, etc. From interpolation calculation of the output value forms, there are mainly the pulse increment interpolation ( Also known as the basic pulse interpolation) And data sampling interpolation. The pulse increment interpolation and data sampling interpolation from one characteristic, this article respectively according to different applications of the developed pulse increment interpolation and data sampling interpolation. 1, the digital integral interpolation digital integral interpolation is one of the pulse increment interpolation. The following will be the first to describe the working principle of the pulse increment interpolation. 2, the pulse increment interpolation pulse increment interpolation is scalar interpolation, interpolation end to create a stroke increment each time, in the form of pulse output. The interpolation algorithm is mainly used in open-loop CNC system, constantly in the process of interpolation calculation to each coordinate axis coordinate feed pulse, drive motor sports. A pulse generated by the axis movement is called the pulse equivalent. Pulse equivalent is the basic unit of the pulse distribution, according to the machining precision of machine tool design, selected ordinary precision machine tool generally take pulse equivalent to: 0. 01 mm, the precision of machine tools to take 1 or 0. 5. Using the pulse increment interpolation algorithm of numerical control system, the main axis feed speed limited by interpolation program running time, general is 1 ~ 3 m/min. The pulse increment interpolation point by point comparison method, data points interpolation method, etc. Point by point comparison method was originally called area criterion, or algebraic operation method, or drunk step approximation method. The principle of this method is that the computer in the control process and point by point to calculate discriminant processing deviation, and to control the feeding, coordinate graphics processing according to the rules out the required artifacts, with step motor or electric hydraulic pulse motor drive machine, the feeding way is step by step, interpolation control machine tool. Point by point comparison method can realize linear interpolation can not only realize circular arc interpolation, its characteristic is operation intuitive, interpolation error is less than one pulse equivalent, uniform output pulse, the speed change is small, convenient adjustment, so the two coordinates is common used in open-loop CNC system. But this method cannot realize multi-axis linkage, the scope of its application is limited by a lot.


Height 143 weight 53
What is the ideal weight for 143 cm tall male or female? Is it normal to weigh 53 kg for this height? Body Mass Index (BMI) will answer these questions. If BMI value is within the range 18.5 – 24.99 (for any height), then the weight is withing normal limits.
|For the height 1.43 meters (143 cm) and for the weight 53 kilograms:|
|Result:||Overweight (not obese).|
|Normal weight limits:||38 - 51 kg.|
|What to do?||Lose 2 kg.|
How to calculate BMI and weight ranges on your own?
- BMI formula: weight / height2
- where the height value is in meters (not in centimeters), for example 1.68 (not 168).
- Multiplication first, then division!
- For example, if the height is 166 cm and the weight is 77 kg, then BMI = 77 / 1.66 * 1.66 = 27.94. BMI above normal values.


Our Numeracy Kit includes three distinct activities which emphasise counting, identifying numbers and number value, practicing simple sums, counting in tens and ones and subitising. The objects can also be used in many other ways as your child explores and leads the play. All three learning activities are aimed at three to six-year-olds and include descriptive information which outlines a targeted learning intention and the skills your child will gain.
There are variations and tips to increase the challenge, depending on individual skill level or age and the kit includes resources and educational aids to facilitate and promote our ‘hands on’ learning approach and to encourage interaction. There’s no printing, laminating or searching for materials – everything your little learner needs is packed in the box ready to go.
Let little hands lead the fun and watch them thrive before your eyes.
THIS KIT INCLUDES:
- 3 x ‘hands on’ activities:
- Thread Counting - Learn to count 1 -10 and practice simple maths
- Peg the Answer - Practice simple addition sums
- Let’s Go Shopping - focuses on practicing counting in tens and ones using grouped and single cork sticks
- 12 x wooden pegs
- 12 x wooden number chips (numbers 1-10 with an addition and minus sign)
- Wooden beads and leather string for threading
- 6 x real life foam vegetables (eggplant, corn, carrot, red capsicum, cucumber, red potato)
- Cork sticks bundled up in groups of tens and extra for ones
- 1 x white board marker
- 1 x number chart from 1-100 (tens column highlighted for extra support when practicing counting in tens)
- Full instructions, challenge tips and additional bonus play ideas; included with each activity
WARNING/CHOKING HAZARD: This pack contains small objects as well as materials made from foam. It is not recommended for children aged 3-years and under or for children who are still mouthing on objects. Please supervise and exercise with caution when little hands are near.
We absolutely love this kit. Every single activity is engaging and fun, and we spend so much time exploring with each activity and resource. Thank you for all the thought you've put into it.
Thank you for making maths fun. My child very much prefers tactical learning as he is more engaged and will complete each task.
We have loved it! He has learnt so much- especially when counting in 10s
I didn’t realise how many activities were in this kit. I originally brought this for my 4 year old to practice numbers and for her to feel as though she was homeschooling too with her brother. She has learnt so much! She can count to 100 using the number chart as a guide, add up sums and has so much fun threading the beads. It has even helped my son who is in grade one practice counting in 10s when solving the maths activities with the vegetables.


I have a problem to calculate a free flooding of offshore subsea pipeline. I would like to calculate it with as minimum aproximations as possible.The calculation is not so simple since the pressure in pipeline is changing as the pipeline is filled with water. The concept is to fill the pipeline from one side (deeper side)and to have a check valve at the other side.
Any equation for a start or a spreadsheet?
There could be several parameters that affect how the calculations could be done.
What will the pipeline contain at the time it is flooded? Such as natural gas, crude oil, gas and oil?
What will be the pipeline's internal pressure profile at the time the valve opens?
What is the pipeline's external pressure profile (depths of the pipeline)?
Before it couldn't be answered generally, since if the air pressure
inside at time of opening was greater than the sea water's pressure
outside, the calculations would have to include a step for pressure
equalization from escaping air from the lowest valve, before you could
assume the remaining air would be displaced to the highest valve(ball valve).
didn't mention the profile. I think its possible that an undulating
pipeline profile may trap air at local high points. That air might lock
at the high points and not free flow to the exit point. Can you assume
there is a continuous constant slope from low to high?
Assuming a continuous slope, that's enough water pressure to compress
the air to roughly 11 barA, or 1/11th of the pipeline's air filled
inside volume at 1 BarA, if you opened the lower valve first without
opening the air escape valve. Infow rate would be whatever the full
open Cv is of the valve times the differential pressure across the valve
at any given time, which would tend to reduce as the pipe filled, with
an inside pressure (P2) = appx = P1 x V1 / V2, where V1 is initial
volume and V2 is the volume of air at any given time. Since pressures
arn't really too significant (compressibility factor of air = 1) I think
you could just assume some reasonable time steps and incrementally
calculate the inside volume, the inside pressure, outside pressure = 10
barG, and get the flowrate across the valve for the next timestep and
arrive at a reasonable approximation to the water filling rate through
that 4" valve. Once the pressures had equalized, you could do the same
thing (kinda' in reverse) with opening the air escape valve and
calculating the airflow rate out as the water displaced it.
From the originalCheck Valve


- This event has passed.
STEAM Lab: Myth-Busting Fun
December 20, 2022 @ 6:00 pm - 6:30 pm
|Recurring Event (See all)
An event every month that begins at 6:00 pm on day Third of the month, repeating until February 21, 2023
Kids ages 8 to 10 will enjoy new science, technology, engineering, art and math activities each month. This series will feature experiments from the book Fairy Tale Science by Sarah Albee.


The Mitten tells the story of a young boy whose grandmother knits him a pair of white mittens. Since the mittens are white, it is easy to lose them in the white of the snow. In fact, the boy does lose one of his mittens. It doesn't take long for a wide variety of woodland animals to make a home inside the warm mitten. Eight animals in total were able to crawl inside the mitten! This was indeed a very special mitten.
After reading the story, we decided to test the capacity of different mittens we brought to the library. The first step was to stuff the mittens with pom poms from our makerspace.
|A student working on fitting a large number of pom poms into a mitten.|
|We had lots of pom poms to use!|
Once the mittens were filled to capacity, we then used our math skills to determine which mitten held the most pom poms. The pom poms were sorted into groups of ten to make counting a bit easier. Math skills used included counting to ten, sorting in groups of ten, and counting by tens.
|Pom poms were sorted into groups of ten.|
Perhaps we were a little overly ambitious with stuffing the mittens. We were able to fit many pom poms into the mittens! We didn't get through all of the counting, but the students certainly made a great dent. Each student counted a large number of pom poms: 50, 50, 70, 100, and 150! The mitten holding the most pom poms was a green alligator mitten which was knitted by Ms. Muhlbauer's mother.
It isn't everyday that we incorporate our math skills in the library, although we hope to be able to do this more often. Students did an outstanding job putting their math skills to work in an interesting way.


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Calculating Your Semester Grade
I'll grant you calculating your Humanities semester grade shouldn't require an advanced degree in math...so here's a form I've created to do it for you! Fill in the appropriate blanks and click "calculate" and your semester class score will be given. Note that the grading scale is listed below, and there is of course no need to round fractions. *
You can also use this to figure out what your future grades need to be as well, or as in the case of dropping a lower score, you can substitute a higher final exam grade for a previous test grade.
80 - 89.99
70 - 79.99
60 - 69.99
59.99 and below
* For those interested in the formula: [(Test 1 + Test 2 + Test 3) / 3 x 2 + Reading Score] / 3 = Final Semester Grade


September 1 was a big day for education data. For starters, the Lujan Grisham Administration released data based on its new assessment (which replaced Susana Martinez’s assessment and then was delayed due to COVID). The results are not pretty. A writeup from the Santa Fe New Mexican both highlights the way the test has evolved and the disappointing results.
In MORE education news, the National Assessment of Educational Progress (NAEP) released nationwide data for 9 year olds. Sadly, “Average scores for age 9 students in 2022 declined 5 points in reading and 7 points in mathematics compared to 2020. This is the largest average score decline in reading since 1990, and the first ever score decline in mathematics.” (see below NM data).
Though (sadly) not broken out by state the NAEP report highlights how COVID lockdowns and chaos impacted students across the country. Since New Mexico students were locked out of their schools by MLG for over a year (6th-most in the nation) there is no doubt that New Mexico students suffered disproportionately due to lost time in the classroom.


Tauchen Sie bei einem virtuellen Rundgang in M. Mathematische Zaubertricks Georg Mayer Was macht ein mathematisches Problem spannend? Die Bildande matematik von Knobelspielen Steven Charlton Die Mathematik von Knobelspielen Steven Charlton.
Geometrie aus dem 3D-Drucker: Joseph Najnudel, mathematician and accomplished pianist, will give a public piano recital on June 13th, beginning at Everybody and their families are cordially invited.
The concert is free of charge. He is also a pianist occasionnally composes music for piano. Geometric quantities of a surface, like distance, angle, or area, change when the surface is deformed.
Euler discovered a quantity, the Euler characteristic, which remains unchanged. The formula of Gauss-Bonnet, a landmark result of mathematics, relates Euler characteristic with geometry. In the talk, I will present ideas of Descartes, Euler, and Gauss related to this formula. Coarse geometry can lead to useful classifications. For example, the word metric on a finitely presented group recognises up to finite groups if that group is the fundamental group of a 3-manifold and it carries a lot of information about the manifold.
I will mainly talk about coarse geometry for complex surfaces, showing that bilipschitz geometry, which is purely topological and ignores any analytic structure, Bildande matematik recover the local analytic structure up to Zariski equisingularity. Joint work with Anne Bildande matematik. When two or three mathematicians
Bildande matematik together to share their ideas on how to attack a problem, sessions can easily stretch out for hours and even days.
The dynamic is not unlike jazz musicians improvising with each spurring the other to "Bildande matematik" farther than they would go alone. Rob Schneiderman was born in Boston, Massachusetts, and raised in California. Rob Schneiderman has released several recordings as leader for the Reservoir Music label.
These CDs contain over twenty Schneiderman originals as well as arrangements of many standards. He has also been on the faculty of The Jazz School in Berkeley. In May Rob Schneiderman received a Ph.
His area of interest is Low-dimensional Topology. He was born and raised in Louisville, Kentucky. He played piano, guitar and electric bass before taking up the double bass at the age of He continues to contribute to the art form as a bassist, bandleader, composer, teacher, clinician and author. J ohn Goldsby is well-known as a jazz educator and currently teaches at the Folkwang-Hochschule in Essen.
He has given jazz workshops all over the world and has written several books on jazz bass techniques. Hans Dekker was born in Boekelo in the Netherlands and began play the drums at the age of nine.
He was introduced to jazz music by his father, who took him to "Bildande matematik" Art Blakey concert. After high school, Hans Dekker studied at the Amsterdam Academy of Music and started working with well-known Dutch and German musicians and orchestras. Hans Dekker has been on the faculty at the Institute of Arts in Enschede since Inthe Dutch graphic artist M. It shows a young man viewing a print in an exhibition gallery.
Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations.
These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank. Hendrik Lenstra received his doctorate from the University of Amsterdam in and became a professor there in In he was appointed to the faculty of the University of California, Berkeley; starting inhe divided his time between Berkeley and the University of Leiden, untilwhen he retired from Berkeley to take a full-time position at Leiden.
He was awarded the Spinoza prize inand on 24 April he was made Knight of the Order of the Netherlands Lion. The story told in this lecture starts with an innocuous little geometry problem, posed in a September blog entry by R. Nandakumar, an engineer from Calcutta, India: I will sketch, however, how this little problem connects to very serious mathematics, including Computational Geometry: This will set up the stage for application of a major tool from Very Pure Mathematicsknown as Equivariant Obstruction Theory.
This is a "cannon", and we'll have fun with shooting it at the sparrow. On the way to a solution, I will try to illustrate the workings of Equivariant Obstruction Theory in a slide show. Combinatorial properties of the permutahedron turn out to be essential.
These will, at the end of the story, "Bildande matematik" us back to India, with some time travel years into the past: But even if the existence problem is solved, the Computational Geometry problem is not: If the solution exists, how do you find one? This problem will be left to you.
Instead, I will comment on the strained relationship between cannons and sparrows, and to this avail quote a poem by Hans Magnus Enzensberger. His current work connects combinatorics and discrete geometry especially polytopes with topology in particular configuration spaces. From tohe was President of the German Mathematical Society. A team of mathematicians is working together on a big project. Excitement of discovery, hope and disappointment, competition and recognition are shown from an infinitely close distance.
Scientists united by the idea of discretization, which, in Bildande matematik, means: The question of where the boundaries lie between mathematics and the lives of those who are involved in it and how much they are willing to sacrifice is as important as the search for Bildande matematik scientific answers.
A unique and unprecedented dive into the unknown world of mathematicians. Entry is free ; there will be time for discussion after the movie.
More information about the movie project can be found here. Was tun Mathematikerinnen und Mathematiker? Weitere Informationen zum Filmprojekt finden Sie hier. This Thursday, January 21st at Everybody from the math community in Bonn and their families are welcome. Habilitation University of
Bildande matematik Visiting Professor, Princeton University The Hirzebruch Lecture is an annual one hour lecture for a general academic audience featuring a prominent speaker, which aims at illustrating the relation between mathematics and other fields like society, art, etc.
It has been established on the occasion of Prof. It is followed by a reception. His talk is drawn from material in and reflections on his recent books, Galileo and with Finn Aaserud Love, literature, Bildande matematik the quantum atom. Niels Bohr's trilogy revisitedboth from Oxford University Press.
The music theorist Thomas Noll, currently a guest at the Max Planck Institute for Mathematics, will give a public lecture about his research on the relation between music and mathematics.
Music theorists emphasize the historical anchors of their field and trace the history of ideas as a substantial part of their collective knowledge. Mathematical investigations offer a complementary approach, where mathematical redefinitions of historically grown concepts are studied with respect to their interdependencies. Within
Bildande matematik last three decades a fruitful dialogue between the two types of investigation emerged.
In my talk, I will share some instances where central elements of traditional knowledge appear in a promising new light after mathematical investigation. Starting from such a definition, various music-theoretically relevant issues around diatonicity can then be re-interpreted on the basis of known facts from algebraic combinatorics on Bildande matematik. But also fundament progressions, a main subject in harmonic tonality, can be revisited in this context.
In addition to the illustrative role of these examples I will attempt to position them within ongoing projects in mathematical music Bildande matematik. The applied mathematical concepts include group actions, monoid actions, algebraic combinatorics on words, formal concept analysis, and discrete Fourier transforms. From - he was the leader of an interdisciplinary research group on mathematical and computational music theory at that same university.
After two years of teaching in theoretical informatics at the TU Berlin he works since as a lecturer in music theory at the Bildande matematik Superior de Musica de Catalunya in Barcelona. He was co-editor of the "Journal of Mathematics and Music" - and serves as reviewer for several journals and conferences in the field. He also is active in popularizing mathematical music theory for a wider audience.
Bildande matematik is a celebration of the story of Ramanujan while walking in his footsteps trying to fathom his genius. I will begin with a very short less than 5 minutes introduction to the making of the documentary. Then we will watch the documentary; it is about one hour Finally, I "Bildande matematik" try to answer any questions the audience might have. The documentary features Ken Ono, Raghuram, K. Srinivasa Rao and T. The documentary also involves conversations with: Often subconsciously artists are drawn to the same structures that fascinate mathematicians as they constantly hunt for interesting new structures to frame their creative process.
Through the work of artists like Borges and Dali, Messiaen and Laban, Professor du Sautoy will explore the hidden mathematical ideas that underpin their creative output and reveal that the work of the mathematician is also driven by strong aesthetic values.
He is author of numerous academic articles and books on mathematics. Der Tag der offenen Tür am MPI für Mathematik ist Teil des bundesweiten 30 -- Vortrag: Die Charakter bildende Kraft der Mathematik (Andrea.
sehnliche Figuren A und B und zWey popularmusicians.info oder sie bildende Seiten a und b so hat man A: B=a'= b“. \ Diese Proportion nebst den Gleichungen in n'a. Bildende Kunst. Visual Art in the ISB-OS is taught in English.
The "Bildande matematik" is designed to offer students a broad and varied experience of Bildande matematik and design.


Maths Supports For Leaving Cert Students
Please see below a list of Maths supports available for students from organisations within our community.
Maths Revision Trinity College Weekend Course
There will be a Maths revision course run in Trinity this Saturday and next Saturday the 23rd and the 30th for both Ordinary and Higher Level students.
The course runs each Saturday on campus with registration from 08:30 - 9:00am and runs until 2:00pm.
The course is discounted for TAP students, 10 euro per day! Please click on the below links to register.
NCI Free Maths and English Easter Revision
NCI are offering free revision sessions for Leaving Cert students in Honours English and Ordinary Maths during the Easter mid-term break.
Project SUMs Pilot Project are offering free Maths grinds on a Tuesday evening from 6pm-8pm in Trinity College Dublin and in TU Tallaght Library for higher ordinary and foundation level students.
Griffith College are also offering free Maths revision on the below dates.
Dublin (Ordinary Level): Saturday, March 23
Dublin (Higher Level): Sunday, March 24
For more information and to register please click here.
Junior Cert and Leaving Cert HL Maths Support Trinity College - TAP Initative.
Maths revision course for Higher Level Maths Students are run every Monday in Trinity College.
Students studying at Junior Cycle will attend from 6.45pm -7.45pm and Leaving Cert Students from 8-9pm and they will both take place in the Joly Lecture Theatre of the Hamilton Building on Campus.
Students will work on exam style problems during the course.
There is a one off fee of €15 which will cover students from now until the end of the year for a weekly grind.
Social media will be updated with other revision courses as we hear about them!


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Time Series Part 2: Forecasting with SARIMAX models: An Intro
This tutorial provide the basics about SARIMAX models in such a way that it helps you understand the working of the algorithm, which is useful if you want to study other forecasting algorithms as well.
In our first tutorial we introduced some basics on time series. In this one we will learn about ARIMA models and their variants SARIMA and ARIMAX : statistical models used for forecasting.
The code of this tutorial can be found at 02-Forecasting_with_SARIMAX.ipynb on GitHub.
After completing this tutorial, you will know:
- What a ARIMA model is
- When to use ARIMA, SARIMA, or ARIMAX
- How to fit (S)ARIMA(X) model
- How to optimize (S)ARIMA(X) model
- How to make forecasts
- How to evaluate the obtained model
The other tutorials about time series, they are available at:
- Time Series Part 1: An Introduction to Time Series Analysis
- Time Series Part 3: Forecasting with Facebook Prophet: An Intro
In this section you will learn about ARIMA models and their variants SARIMA and ARIMAX.
ARIMA means Auto Regressive Integrated Moving Average. It is a combination of two models: AR (Auto Regressive) model which uses lagged values of the time series to forecast and MA (Moving Average) model that uses lagged values of residual errors to forecast. In other words, this model uses dependencies both between data values and errors values from the past to optimize the predictions.
ARIMA uses three parameters – ARIMA(p,d,q):
- Auto Regressive term p: Number of autoregressive lags.
- Order of differencing term d: Number of times differencing pre-processing step is applied to make the time series stationary.
- Moving Average term q: Number of moving average lags.
We cannot model a time series if it is not stationary. However, we can apply some transformation such as differencing to make a time series stationary, as seen in the previous tutorial. The parameter d allow us to apply differencing within ARIMA.
It is also possible to apply transformations before applying ARIMA in order to make time series stationary. However, when applying differencing in this way we are forecasting on the transformed data, therefore we need to reverse the transformation in order to access the forecast of the original values.
It is also possible to extend the ARIMA model to use exogenous inputs and create an ARIMAX model. In this model the time series is modeled using other independent variables as well as the time series itself.
For example, when modeling the waiting time in an emergency room. The number of nurses available at a certain shift could be considered an external variable since it may have impact on the waiting time. If this is indeed the case, we can affect the waiting times by changing the number of nurses .
If there is seasonality visible in a time series dataset, a SARIMA (Seasonal ARIMA) model should be used. When applying an ARIMA model, we are ignoring seasonality and using only part of the information in the data. As a consequence, we are not making the best predictions possible.
SARIMA models include extra parameters related to the seasonal part. Indeed, we can see a SARIMA model as two ARIMA models combined: one dealing with non-seasonal part and another dealing with the seasonal part.
Therefore, a SARIMA(p,d,q)(P,D,Q,S) model have all the parameters described above (non-seasonal parameters) and P,D,Q,S that are the seasonal parameters, i.e.,
- p: Autoregressive order.
- d: Differencing order.
- q: Moving average order.
- P: Seasonal autoregressive order.
- D: Seasonal differencing order.
- Q: Seasonal moving average order
- S: Length of the seasonal cycle.
Now time for some hands-on examples to illustrate these models.
The Walmart Dataset
This data consists of 5 years of store-item sales data split in a training dataset (train.csv) and a test dataset (test.csv). The objective of this competition was to forecast 3 months of sales for 50 different items at 10 different stores using the 5 years history of sales.
Our goal here is to use part of this data to apply what we have learnt about time series and the forecast methods introduced during this tutorial.
Both train and test datasets have 10 stores and each store offers 50 unique items, and sales is our target.
The training dataset has data from January 1st, 2013 until December 31st, 2017. The goal is to predict sales of items in all stores from January 1st, 2018 until March 31st, 2018, i.e., 3 months.
As we can see, store 2 has the highest volume of sales. Which products are the most sold there?
The most sold item in store 2 is item 28 with 205677 units sold . Item 15 comes in second with 205569 units sold.
From the box-plots above we can conclude:
- Higher sales occur during the weekend (5=Saturday, 6=Sunday).
- Higher volume in sales is achieved in July and lowest in January
- This pattern of sales per month seems to be pretty the same every year.
To learn applying (S)ARIMA(X) models we will follow some steps based on Box-Jenkins Method. This popular framework provides a systematic way that involves getting to know your time series data and applying the appropriate methods to choose parameters that will lead to a good model.
STEP1 : Identify
Following the schema above in this step we use tools to identify characteristics of the time series so we can build an appropriate model.
Here we search for answers for questions such as:
- Is the time series stationary?
- If not stationary, which transformation should we apply to make it stationary?
- Is the time series seasonal?
- If seasonal what is the seasonal period?
- Which orders to use? (p for AR, q for MA)
Visualize times series sales of item 28 at store 2
As we saw previously in this data, we have 500 time series which are defined by the pair store-item. Here we are working with forecasting individual time series. To forecast sales for all stores and all items we need to apply a forecast model to each one of the time series.
For the purpose of demonstrating the use of these models, we will work with only one time series in this tutorial: sales of item 28 (the most sold item) at store 2 (the store with the highest number of sales).
From the decomposition above we can conclude:
- There is a upward trend on sales. Therefore, this time series is not stationary.
- From the seasonal component we can observe that the model is additive, since the seasonal component is similar (not getting multiplied) over the period of time.
- Also, we can observe on the seasonal component seasonality in sales with lower sales in January and higher sales in July.
Since our data is not stationary, we need to answer What differencing will make it stationary? For this we will use our obtain_adf_kpss_results function to find out how many times we need to apply differencing in order to make this time series stationary. This will be our parameter d for the ARIMA model.
Apply Stationarity Tests
Results of stationary tests show that applying differencing only once is enough to make our time series is stationary, i.e., d=1 .
Plot ACF and PACF
Autocorrelation and Partial autocorrelation plots are heavily used in time series analysis and forecasting. They can give clues about promising values of ARIMA parameters. It also can show us if we need to apply differencing or if we have applied it too much.
AutoCorrelation Function – ACF is the plot of the autocorrelation of a time series by lag. This plot is sometimes called a correlogram. It includes direct and indirect dependence information. In simple terms, ACF describes how well the present value of the series is related with its past values. The bars of the ACF plot represent the ACF values at increasing lags. The blue shaded area represents the confidence interval, which is set to 95% by default. If the bars lie inside the blue shaded region, then they are not statistically significant.
Different from ACF, Partial AutoCorrelation Function – PACF only describes the direct relationship between an observation and its lag. Basically, instead of finding correlations of present with lags like ACF, it finds correlation of the residuals (which remains after removing the effects which are already explained by the earlier lag(s)).
So how these plots can help us finding p (AR term) and q (MA term)?
As said earlier, ACF and PACF can also give tips about differencing.
It is important to made the time series stationary before making these plots. If the ACF values are high and trail off very slowly this is a sign that the data is non-stationarity, so it needs to be differenced.
If the autocorrelation at lag-1 is very negative this is a sign that we have taken the difference too many times.
We know that our time series is not stationary and need to be differenced. Let’s plot ACF and PACF for the original and differenced time series.
By observing the ACF and PACF plots after making the time series stationary, we can infer from the ACF plots that there is a seasonal behaviour of period 7 which is clear by the picks at lag 7, 14, 21 etc. (every week). This shows us the need of a seasonal term in our ARIMA model. In other words, we need a SARIMA model.
STEP 2 : Estimate Coefficients (p,q)
Although we had clear signs that we need a SARIMA model, we will start by applying a ARIMA model instead. By doing so we can obtain a better understanding on the differences between ARIMA and SARIMA when applying the Box-Jenkins’s method. In addition, it will be clear what the advantages are of choosing the appropriate model.
ACF and PACF plots can help us find appropriate values for parameters p and q . However, the interpretation of these plots is not always clear. To obtain more assurance to our choices we can apply an empirical method. This method consists on fitting the ARIMA model for different values of p and q, and choosing the best value based on metrics such as AIC and BIC.
AIC (Akaike information criterion) is a metric which tells us how good a model is. Lower the value, better the model. The AIC also penalizes models which have lots of parameters. This means if we set the order too high compared to the data, we will get a high AIC value. This stops us overfitting to the training data.
BIC (Bayesian information criterion) is similar to AIC, therefore lower value means a better model. However, BIC penalizes additional model orders more than AIC. As consequence, BIC will sometimes suggest a simpler model.
After fitting a model, we can access its summary statistics, and that is where we can find the values of AIC and BIC.
Usually there is agreement between AIC and BIC. If there is no agreement, you should choose a smaller AIC if you prefer a predictive model. Otherwise, choose smaller BIC for an explanatory model.
Check the how to obtain the summary statistics in the following example.
Now let’s scan different values of p and q and choose the values that points to smaller AIC and/or BIC.
The results above show that both AIC and BIC agree that the best model in this case should be ARIMA(4,1,5).
STEP 3: Model Evaluation
Before, using a model we want to know how accurate it is. Here we present some tools to evaluate the model before considering it the best one and putting it to production.
For this evaluation we focus on the residuals. The residuals are the difference between the model’s one-step-ahead predictions and the real values of the time series.
Mean Absolute Error (MAE)
We start by calculating the Mean Absolute Error (MAE) of the residuals. This will give us an idea of how far, on average, the predictions are from the true values.
MAE = 4.73, i.e., the mean average error is about 5 sales per day where the average sale of item 28 in store 2 is in average 28 sales per day. Can we do better than this?
For an ideal model the residuals should be uncorrelated with Gaussian noise centered on zero. Therefore, continuing our model evaluation we use tools that allow us to check if it is true.
Diagnostic Summary Statistics
Another important tool to evaluate the model is the analysis of the residual test statistics in the results summary.
Now we evaluate Prob(Q) and Prob(JB) applying, respectively, the following tests:
Null hypothesis: There are no correlations in the residuals.
Null hypothesis: Residuals are normally distributed.
Prob(Q) = 0.88 > 0.05. We shouldn’t reject the null hypothesis that the residuals are uncorrelated so the residuals are not correlated.
Prob(JB) = 0.02 < 0.05. We reject the null hypothesis that the residuals are normally distributed. Therefore, the residuals are not normally distributed.
In addition, there are 4 common plots to help us deciding whether a model is a good fit for the data in question.
For an ideal model the residuals should be uncorrelated with Gaussian noise centered on zero. By analyzing the plots above having this in mind we can evaluate if we have a good model or not.
So, let’s analyze those plots (Clockwise from left-top plot):
- Standardized residual: There are no obvious patterns in the residuals. This is our case which points out to a good model
- Histogram plus kde estimate: The histogram shows the measured distribution of the residuals while the orange line shows the KDE curve (smoothed version of the histogram). The green line shows a normal distribution. For a good model the orange line should be similar to the green line. The orange curve is not very similar to the green one.
- Correlogram or ACF plot: 95% of correlations for lag greater than one should not be significant (inside the blue area). This is also the case, i.e., good model.
- Normal Q-Q: Most of the data points should lie on the straight line, indicating a normal distribution of the residuals. This happens here.
Therefore, all in all the model pointed by our empirical search seems to be a good model.
- If the residuals are not normally distributed try to increase d.
- If the residuals are correlated try to increase p or q.
ACF Plot to Determine Seasonal Period
Previously, we got a hint from the ACF plot that our time series has a seasonal period of 7, i.e., S=7.
Therefore, the ACF plot can help in finding out the time period, especially if it is not clear from the plots of the time series.
Important: Make time series stationary first.
The non-seasonal ACF and PACF plots (2) above show MA model pattern with q=1.
The Seasonal ACF and PACF plots (3) look like an MA(1) model, i.e., Q=1. We could select the model that combines both of these, i.e., SARIMA(0,1,6)(0,1,1)7.
The following code shows how to fit this model and obtain the MAE of the residuals:
MAE = 4.555 which is a bit lower than the ARIMA model, but is this a good model, i.e., residuals are not correlated and normally distributed?
Both summary and diagnostic plots agree that residuals are uncorrelated and normally distributed which points for a good model. Even the histogram looks better than the previous one with the orange curve closer to the green one.
Automated Model Selection
pmdarima allows us to automate the search of model orders. We use information we got from the Box-Jenkins identification step to predefine some of the orders before we fit. Automated Model Selection can speed up the process of choosing model orders, but needs to be done with care. Automation can make mistakes since the input data can be imperfect and affect the test scores in non-predictable ways.
The only non-optional parameter in auto_arima is data. However, using your knowledge to specify other parameters can help finding the best model.
After running the code above, automated model selection pointed out SARIMA(6,1,1)(6,1,0)7 as best model based on AIC.
For now on let’s call sarima_01_model the first SARIMA model obtained by observing ACF and PACF plots (i.e., SARIMA(0,1,6)(0,1,1)7) and sarima_02_model the second model obtained using automated model selection SARIMA(6,1,1)(6,1,0)7.
Comparing sarima_01_model and sarima_02_model: the kde curve of sarima_01_model is closer to a normal distribution than the kde curve of sarima_02_model. In addition, sarima_01_model has smaller MAE, 4.55 against 4.788 MAE obtained by sarima_02_model.
This would point us to choose sarima_01_model as the most promising model.
Forecasting with SARIMAX
SARIMA vs ARIMA forecasts
We will continue using both ARIMA and SARIMA models even if we know that SARIMA, in this case, is the most adequate model. The goal here is to show why SARIMA is the most adequate.
Forecast in Sample
To have a feeling on how good the chosen models are doing we will take the last 90 days in training dataset as validation data.
Metrics Used to Compare Models
The models presented here and in the third part of this tutorial will be evaluated using MAE (Mean Absolute Error) and MAPE (Mean Absolute Percentage Error). These are popular metrics when evaluating regression models and you will come often across MAE and MAPE when evaluating forecasting models.
When comparing forecast methods applied to a single time series, or to several time series with the same units, MAE is popular as it is easy to both understand and compute. Percentage errors measures such as MAPE have the advantage of being unit-free, and so are frequently used to compare forecast performances between data sets.
Before comparing our models using those metrics let’s revisit their summary statistics.
The three models seem to present no correlation in the residuals. The ARIMA model is the only one where residuals are NOT normally distributed. according to Jarque_Bera (Prob(JB) < 0.05). When observing values of AIC and BIC, SARIMA(0,1,6)(0,1,1)7 has the smallest values which also points to a better model.
Let’s see what forecast in-sample tells us.
For our forecasting in sample, we use the method get_prediction using the last days of the training data as validation data. After that we use mean_absolute_error and mean_absolute_percentage_error from sklearn.metrics to obtain MAE and MAPE for all three models.
MAE and MAPE for these three models are:
When considering MAE and MAPE the SARIMA model chosen by automated selection has the smallest values, i.e., this model has the best accuracy.
Let’s check graphically the observed values against the predictions.
Observe how the result of the SARIMA(6,1,1)(6,1,0)7 model (green line) follows better the red curve (observed values) than the ARIMA model (blue line) and the other SARIMA model (SARIMA(0,1,6)(0,1,1)7, orange line).
Forecast Out of Sample
Let’s predict 90 days ahead. For this part we will just use the ARIMA model (ARIMAX(4,1,5)) and the SARIMA model chosen by automated model selection: SARIMA(6,1,1)x(6,1,0)7.
Notice that now we use get_forecast in place of get_predict.
The plot below shows again that the result obtained by SARIMA model follows better the observed time series. Remember, the ARIMA model completely ignores the seasonal information which explains in great deal such difference between these two models.
Once the best model is found, it is useful to know how to save it. For this we use the joblib library.
Since, the second SARIMA model was the one showing best results, we choose to save it.
To load the saved model use .load() as follows:
Conclusions about SARIMAX models
In this section we introduced ARIMA models and its variants: Seasonal ARIMA (SARIMA) and ARIMAX which uses external data (exogenous inputs) to improve the performance of the ARIMA model.
We followed the Box-Jenkins method to find the best model considering a part of our dataset (time series of sales of product 28 of Walmart’s store 2). As first step, we’ve identified important characteristics of our time series such as stationarity and seasonality.
Then, we also used graphical and statistical methods such as follows to find the best fit model:
- Augmented Dickey-Fuller test,
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test,
- ACF and PACF plots analysis,
- Exploring model summary statistics,
- Analyze plots obtained using the statsmodel method plot_diagnostics.
Once we’ve found a model considered good, we used it to forecast in sample, i.e., we applied the model on part of the training data as validation data. Like this, we were able to have a feeling of how good the model is. After that we forecast out of the sample, i.e., 90 days in future.
Both the application of the Box-Jenkins Method as well as using the chosen model to forecast was applied on ARIMA and SARIMA models.
We knew since the beginning that the most appropriate model would be a SARIMA model since we were dealing with a seasonal time series. However, working with both models gave us the opportunity to see the nuances in the application of the Box-Jenkins for these two types of models. Moreover, we could see clearly that if seasonality is not considered we are not using all information and therefore not making the best predictions possible. This became clear also from the forecasting plots.
We didn’t provide an explicit example of (S)ARIMAX, i.e., an (S)ARIMA model using external data. Therefore, I suggest trying to improve the best model by adding holidays as external data. Here you have an example using exogenous regressor. The holidays Python library helps you obtaining holidays.


Saxon Math is the core mathematics program for Fenton Primary Center and Pearson Scott Foresman is the core program for Fenton Avenue Charter School. Both were adopted as the core math programs during the 2007-2008 California math adoption cycle and were implemented for the 2008-2009 school year. Both series’ incorporates the five strands of mathematics (number sense; algebra and functions; measurement and geometry; statistics, data analysis and probability; and mathematical reasoning) and is aligned with the Content Standards for California Public Schools.
Site-licensed software, the Saxon Math and enVision web sites, and teacher-designed computer activities will continue to enhance and improve students’ understanding by providing individualized activities to reinforce skills and concepts and foster deeper mathematical learning.
Every year, all grade levels have met Annual Measurable Objectives (AMOs) for mathematics on the California Standards Test confirming the alignment of the program with state standards and the effectiveness of the adoption in meeting the needs of the Charter School’s student population.


How much will Ripple cost in a month, in a year? Is it worth investing in Ripple now? Is Ripple and other cryptocurrency good an investment? Will the crypto boom and Bull rally be repeated?
It is very difficult to predict. But our portal has developed a unique mathematical model for predicting the cryptocurrency market. The accuracy of forecasts is 85-95%. When analyzing the market, all factors affecting Ripple and the market as a whole are taken into account.
For this page, the monthly forecast for 2020 is presented. The table shows the average, minimum and maximum prices for each month. And monthly volatility.
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I introduced a new game with my 8th graders yesterday. It is always hard to know whether a game will be a hit or a flop, so I was surprised by the enthusiasm with which they received this very simple activity.
The instructions are very simple: the students are to count a range of numbers, say from 1 -20, 100 and up or whatever you choose (I am also planning to use letters of the alphabet, simple German verb conjugations etc.). Instead of having an order of which student goes when, they are to say the number out when it feels like it's their turn. The only rule is that if two students speak at the same time, they have to start over.
As I was watching the 8th grade, I saw just how deeply this game meets the children. For one, it is a rhythmical activity which helps them relax into class. They also have to get very still, listening to each other. This prepares them extremely well for the rest of class. Finally, the children love a challenge, and this game sets the tone for trying to do better all the time, an element that I have found can be challenging for some of the students.
So this one was a winner which we will be playing regularly.


ALGEBRA 1 · GEOMETRY · ALGEBRA 2 · PRECALCULUS · CALCULUS · STATISTICS
The Lick-Wilmerding High School Mathematics Department strives to empower students to interact with mathematics so they can experience the power and beauty of the subject. We teach students to approach math as a way of thinking, with the focus on inquiry, sense-making, reasoning and application. In each class, students have the opportunity to collaborate, persist, and seek multiple approaches in order to become more flexible and strategic problem solvers. Students develop a learning mindset by reflecting on mistakes and viewing them as opportunities for growth. With this mindset, students know that they can learn any mathematics they may need to achieve their goals in life.


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Money Rush is a quick reflex game that moves coins into math operations in your favor. Convert coins to cash to unlock chain stores to earn super profits.
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