Articles

37.1: Youtube - Mathematics


37.1: Youtube - Mathematics

Can I upload full playthroughs onto YouTube?

Is it OK to post long gameplay (playthroughs) captured videos on YouTube, of games such as: Outlast, Outlast 2, WoW, Among Us, Cattails, Dead Space, etc.

Or are these videos going to be removed from YouTube and the channel penalized?

Or are some games/companies OK with people posting playthroughs, while other games/companies are actively against it? And if so, which ones are OK with it?


Mathematics

Lander’s mathematics curriculum offers a great deal of flexibility, centering on a core of math courses that are balanced with a mix of liberal arts classes, math electives and general electives.

As a math major, you will build a solid foundation in calculus, differential equations and fundamentals of logic before progressing to studies in linear and abstract algebra, mathematical analysis and statistics. You can use your major electives to explore geometry, complex analysis or the history of mathematics.

Mathematics Honors Program

Students majoring in mathematics may earn a “BS Degree with Honors” in mathematics. To qualify, a student must meet the following conditions:

  1. In addition to the normal course requirements for a BS degree in mathematics, the student must complete the following courses:
    MATH 432 and MATH 422, with a total of 30 credits of coursework in mathematics at the 300-level or above.
  2. The student must complete six semester hours of a college level language. This language may not be English or the student’s native language.
  3. The student must submit a project proposal no later than January 15 of the junior year. The proposal must be approved by a majority of the full-time mathematics faculty and result in a finished product of sufficient quality to:
    a) Receive a grade of “A” or “B” (MATH 390) and
    b) Be accepted for publication or presented at a meeting of a mathematical society or be presented as a seminar to mathematics faculty, students, and guests.
  4. Upon graduation, the student must have a cumulative GPA of 3.5 or better in both overall coursework and in mathematics coursework.

NOTE: In lieu of requirement 1 above, the student may complete an engineering degree at Clemson University under the engineering/mathematics dual-degree program. The student may then substitute an approved engineering project at Clemson for requirement 3 above.

Special situations may require a deviation from these requirements (such as for students seeking teacher certification in mathematics or those in the engineering program). All deviations must be approved by a majority of the mathematics faculty.

Transfer students who wish to pursue an Honors Program in Mathematics must spend at least four full-time semesters (fall or spring) at Lander University and complete at least 21 semester hours of mathematics courses at Lander University. They must also have an overall GPA of 3.5 on all courses transferred and a GPA of 3.5 on mathematics courses transferred.

PROGRAM REQUIREMENTS

Note:The information below provides convenient links to some of the courses required for this degree however, it should not be used as a course registration guide. Please refer to the official Lander University Academic Catalog for the most accurate and up-to-date program requirements.

Single Variable Calculus I

B. Humanities and Fine Arts
(6 hours selected from 2 different disciplines)

United States History to 1877
OR POLS 101 American National Government

MAJOR PROGRAM CORE REQUIREMENTS CREDIT
HOURS
MATH 241 Calculus III 4
MATH 242 Differential Equations 4
MATH 308 Linear Algebra 3
MATH 311 Mathematical Statistics 3
MATH 499 Capstone 1

MAJOR PROGRAM ADDITIONAL REQUIREMENTS CREDIT
HOURS
CIS 130 Problem Solving and Programming Methods 4
MATH 134 Introduction to Mathematical Proof 3
MATH 421 Abstract Algebra I 3
MATH 431 Analysis I 3
MATH 422 Abstract Algebra II
OR MATH 432 Complex Analysis
3

300-level or above Mathematics content courses except MATH 450 or MATH 451


How to Multiply or Divide Feet & Inches

The steps to multiply or divide feet and inches are similar to the steps for adding and subtracting above.

Step One: Convert Feet and Inches to Decimal

The first step in multiplying or dividing is to convert the length measurements to a decimal value. If the length measurements are in feet and inches, it might be easiest to convert to inches.

Step Two: Multiply or Divide

With the length value converted to a decimal, it’s now possible to multiply or divide just like you would with any decimal number. For example, if your inch value is 1.25 and you need to multiply by 2, simply multiply using 1.25 × 2 = 2.5 .

The following charts make multiplying or dividing fractional inch values much easier.


Euler&rsquos Answer

Shockingly, Leonard Euler had very little to do with the number e outside of attaching its memorable namesake. His one, true, technical contribution came from proving that e is irrational by re-writing it as a convergent infinite series of factorials:

His second contribution, the core reason the constant bears his initial, is simply because he famously used the constant in a letter to a colleague & historically declared it as e. It&rsquos now a happy coincidence that &ldquoe&rdquo is the first letter in exponential, however, the jury is still out on whether he purposefully named it after himself. The truth may be even more prosaic: Euler was using the letter a in some of his other mathematical work, and e was the next vowel.

Whatever the reason, the notation e made its first appearance in a letter Euler wrote to Goldbach in 1731. He made various discoveries regarding e in the following years, but it was not until 1748 when Euler published Introductio in Analysin infinitorum that he gave a full treatment of the ideas surrounding e.


Subpart 37.4 - Nonpersonal Health Care Services

37.400 Scope of subpart.

This subpart prescribes policies and procedures for obtaining health care services of physicians, dentists and other health care providers by nonpersonal services contracts, as defined in 37.101.

37.401 Policy.

Agencies may enter into nonpersonal health care services contracts with physicians, dentists and other health care providers under authority of 10 U.S.C.2304 and 41 U.S.C.chapter 33, Planning and Solicitation. Each contract shall-

(a) State that the contract is a nonpersonal health care services contract, as defined in 37.101, under which the contractor is an independent contractor

(b) State that the Government may evaluate the quality of professional and administrative services provided, but retains no control over the medical, professional aspects of services rendered (e.g., professional judgments, diagnosis for specific medical treatment)

(c) Require that the contractor indemnify the Government for any liability producing act or omission by the contractor, its employees and agents occurring during contract performance

(d) Require that the contractor maintain medical liability insurance, in a coverage amount acceptable to the contracting officer, which is not less than the amount normally prevailing within the local community for the medical specialty concerned and

(e) State that the contractor is required to ensure that its subcontracts for provisions of health care services, contain the requirements of the clause at 52.237-7, including the maintenance of medical liability insurance.

37.402 Contracting officer responsibilities.

Contracting officers shall obtain evidence of insurability concerning medical liability insurance from the apparent successful offeror prior to contract award and shall obtain evidence of insurance demonstrating the required coverage prior to commencement of performance.

37.403 Contract clause.

The contracting officer shall insert the clause at 52.237-7, Indemnification and Medical Liability Insurance, in solicitations and contracts for nonpersonal health care services. The contracting officer may include the clause in bilateral purchase orders for nonpersonal health care services awarded under the procedures in part 13.


37.1: Youtube - Mathematics

Today, November 30 th , is AMS Day! Join our celebration of AMS members and explore special offers on AMS publications, membership and more. Offers end 11:59pm EST.

ISSN 1088-6842(online) ISSN 0025-5718(print)

The error term in the prime number theorem


Authors: David J. Platt and Timothy S. Trudgian
Journal: Math. Comp. 90 (2021), 871-881
MSC (2020): Primary 11N05, 11N56 Secondary 11M06
DOI: https://doi.org/10.1090/mcom/3583
Published electronically: November 16, 2020
MathSciNet review: 4194165
Full-text PDF
View in AMS MathViewer

Abstract: We make explicit a theorem of Pintz, which gives a version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing problem concerning an inequality studied by Ramanujan.

  • Christian Axler, Estimates for $pi (x)$ for large values of $x$ and Ramanujan’s prime counting inequality, Integers 18 (2018), Paper No. A61, 14. MR 3819880
  • Bruce C. Berndt, Ramanujan’s notebooks. Part IV, Springer-Verlag, New York, 1994. MR 1261634
  • S. Broadbent, H. Kadiri, A. Lumley, N. Ng, and K. Wilk, Sharper bounds for the Chebyshev function $ heta (x)$, Preprint available at arXiv:2002.11068.
  • Jan Büthe, An analytic method for bounding $psi (x)$, Math. Comp. 87 (2018), no. 312, 1991–2009. MR 3787399, DOI https://doi.org/10.1090/mcom/3264
  • Jan Büthe, Estimating $pi (x)$ and related functions under partial RH assumptions, Math. Comp.85 (2016), no. 301, 2483–2498. MR 3511289, DOI https://doi.org/10.1090/S0025-5718-2015-03060-9
  • M. Cully-Hugill and T. Trudgian, Two explicit divisor sums, To appear in Ramanujan J., preprint available at arXiv:1911.07369.
  • Yannick Saouter, Timothy Trudgian, and Patrick Demichel, A still sharper region where $pi (x)-< m li>(x)$ is positive, Math. Comp.84 (2015), no. 295, 2433–2446. MR 3356033, DOI https://doi.org/10.1090/S0025-5718-2015-02930-5
  • Adrian W. Dudek, An explicit result for primes between cubes, Funct. Approx. Comment. Math. 55 (2016), no. 2, 177–197. MR 3584567, DOI https://doi.org/10.7169/facm/2016.55.2.3
  • Adrian W. Dudek and David J. Platt, On solving a curious inequality of Ramanujan, Exp. Math. 24 (2015), no. 3, 289–294. MR 3359216, DOI https://doi.org/10.1080/10586458.2014.990118
  • P. Dusart. Autour de la fonction qui compte le nombre de nombres premiers. PhD thesis, Université de Limoges, 1998.
  • Pierre Dusart, Explicit estimates of some functions over primes, Ramanujan J. 45 (2018), no. 1, 227–251. MR 3745073, DOI https://doi.org/10.1007/s11139-016-9839-4
  • Laura Faber and Habiba Kadiri, Corrigendum to New bounds for $psi (x)$ [ MR3315511], Math. Comp. 87 (2018), no. 311, 1451–1455. MR 3766393, DOI https://doi.org/10.1090/mcom/3340
  • Kevin Ford, Zero-free regions for the Riemann zeta function, Number theory for the millennium, II (Urbana, IL, 2000) A K Peters, Natick, MA, 2002, pp. 25–56. MR 1956243
  • A. E. Ingham, The distribution of prime numbers, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1990. Reprint of the 1932 original With a foreword by R. C. Vaughan. MR 1074573
  • Habiba Kadiri, A zero density result for the Riemann zeta function, Acta Arith. 160 (2013), no. 2, 185–200. MR 3105334, DOI https://doi.org/10.4064/aa160-2-6
  • Habiba Kadiri, Allysa Lumley, and Nathan Ng, Explicit zero density for the Riemann zeta function, J. Math. Anal. Appl. 465 (2018), no. 1, 22–46. MR 3806689, DOI https://doi.org/10.1016/j.jmaa.2018.04.071
  • Michael J. Mossinghoff and Timothy S. Trudgian, Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function, J. Number Theory 157 (2015), 329–349. MR 3373245, DOI https://doi.org/10.1016/j.jnt.2015.05.010
  • J. Pintz, On the remainder term of the prime number formula. II. On a theorem of Ingham, Acta Arith. 37 (1980), 209–220. MR 598876, DOI https://doi.org/10.4064/aa-37-1-209-220
  • David J. Platt, Isolating some non-trivial zeros of zeta, Math. Comp. 86 (2017), no. 307, 2449–2467. MR 3647966, DOI https://doi.org/10.1090/mcom/3198
  • D. J. Platt and T. S. Trudgian, On the first sign change of $ heta (x)-x$, Math. Comp.85 (2016), no. 299, 1539–1547. MR 3454375, DOI https://doi.org/10.1090/S0025-5718-2015-03021-X
  • D. J. Platt and T. S. Trudgian, The Riemann hypothesis is true up to $3cdot 10^<12>$, Submitted. Preprint available at arXiv:2004.09765.
  • J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 137689
  • J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $ heta (x)$ and $psi (x)$, Math. Comp.29 (1975), 243–269. MR 457373, DOI https://doi.org/10.1090/S0025-5718-1975-0457373-7
  • Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $ heta (x)$ and $psi (x)$. II, Math. Comp.30 (1976), no. 134, 337–360. MR 457374, DOI https://doi.org/10.1090/S0025-5718-1976-0457374-X
  • Aleksander Simonič, Explicit zero density estimate for the Riemann zeta-function near the critical line, J. Math. Anal. Appl. 491 (2020), no. 1, 124303, 41. MR 4114203, DOI https://doi.org/10.1016/j.jmaa.2020.124303
  • Tim Trudgian, Updating the error term in the prime number theorem, Ramanujan J. 39 (2016), no. 2, 225–234. MR 3448979, DOI https://doi.org/10.1007/s11139-014-9656-6
    References
  • Christian Axler, Estimates for $pi (x)$ for large values of $x$ and Ramanujan’s prime counting inequality, Integers 18 (2018), Paper No. A61, 14. MR 3819880
  • Bruce C. Berndt, Ramanujan’s Notebooks. Part IV, Springer-Verlag, New York, 1994. MR 1261634
  • S. Broadbent, H. Kadiri, A. Lumley, N. Ng, and K. Wilk, Sharper bounds for the Chebyshev function $ heta (x)$, Preprint available at arXiv:2002.11068.
  • Jan Büthe, An analytic method for bounding $psi (x)$, Math. Comp. 87 (2018), no. 312, 1991–2009. MR 3787399, DOI https://doi.org/10.1090/mcom/3264
  • Jan Büthe, Estimating $pi (x)$ and related functions under partial RH assumptions, Math. Comp. 85 (2016), no. 301, 2483–2498. MR 3511289, DOI https://doi.org/10.1090/mcom/3060
  • M. Cully-Hugill and T. Trudgian, Two explicit divisor sums, To appear in Ramanujan J., preprint available at arXiv:1911.07369.
  • Yannick Saouter, Timothy Trudgian, and Patrick Demichel, A still sharper region where $pi (x)-
  • >(x)$ is positive, Math. Comp. 84 (2015), no. 295, 2433–2446. MR 3356033, DOI https://doi.org/10.1090/S0025-5718-2015-02930-5
  • Adrian W. Dudek, An explicit result for primes between cubes, Funct. Approx. Comment. Math. 55 (2016), no. 2, 177–197. MR 3584567, DOI https://doi.org/10.7169/facm/2016.55.2.3
  • Adrian W. Dudek and David J. Platt, On solving a curious inequality of Ramanujan, Exp. Math. 24 (2015), no. 3, 289–294. MR 3359216, DOI https://doi.org/10.1080/10586458.2014.990118
  • P. Dusart. Autour de la fonction qui compte le nombre de nombres premiers. PhD thesis, Université de Limoges, 1998.
  • Pierre Dusart, Explicit estimates of some functions over primes, Ramanujan J. 45 (2018), no. 1, 227–251. MR 3745073, DOI https://doi.org/10.1007/s11139-016-9839-4
  • Laura Faber and Habiba Kadiri, Corrigendum to New bounds for $psi (x)$ [ MR3315511], Math. Comp. 87 (2018), no. 311, 1451–1455. MR 3766393, DOI https://doi.org/10.1090/mcom/3340
  • Kevin Ford, Zero-free regions for the Riemann zeta function, Number theory for the millennium, II (Urbana, IL, 2000) A K Peters, Natick, MA, 2002, pp. 25–56. MR 1956243
  • A. E. Ingham, The Distribution of Prime Numbers, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1990. Reprint of the 1932 original With a foreword by R. C. Vaughan. MR 1074573
  • Habiba Kadiri, A zero density result for the Riemann zeta function, Acta Arith. 160 (2013), no. 2, 185–200. MR 3105334, DOI https://doi.org/10.4064/aa160-2-6
  • Habiba Kadiri, Allysa Lumley, and Nathan Ng, Explicit zero density for the Riemann zeta function, J. Math. Anal. Appl. 465 (2018), no. 1, 22–46. MR 3806689, DOI https://doi.org/10.1016/j.jmaa.2018.04.071
  • Michael J. Mossinghoff and Timothy S. Trudgian, Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function, J. Number Theory 157 (2015), 329–349. MR 3373245, DOI https://doi.org/10.1016/j.jnt.2015.05.010
  • J. Pintz, On the remainder term of the prime number formula. II. On a theorem of Ingham, Acta Arith. 37 (1980), 209–220. MR 598876, DOI https://doi.org/10.4064/aa-37-1-209-220
  • David J. Platt, Isolating some non-trivial zeros of zeta, Math. Comp. 86 (2017), no. 307, 2449–2467. MR 3647966, DOI https://doi.org/10.1090/mcom/3198
  • D. J. Platt and T. S. Trudgian, On the first sign change of $ heta (x)-x$, Math. Comp. 85 (2016), no. 299, 1539–1547. MR 3454375, DOI https://doi.org/10.1090/mcom/3021
  • D. J. Platt and T. S. Trudgian, The Riemann hypothesis is true up to $3cdot 10^<12>$, Submitted. Preprint available at arXiv:2004.09765.
  • J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 137689
  • J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $ heta (x)$ and $psi (x)$, Math. Comp. 29 (1975), 243–269. MR 457373, DOI https://doi.org/10.2307/2005479
  • Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $ heta (x)$ and $psi (x)$. II, Math. Comp. 30 (1976), no. 134, 337–360. MR 457374, DOI https://doi.org/10.2307/2005976
  • Aleksander Simonič, Explicit zero density estimate for the Riemann zeta-function near the critical line, J. Math. Anal. Appl. 491 (2020), no. 1, 124303, 41. MR 4114203, DOI https://doi.org/10.1016/j.jmaa.2020.124303
  • Tim Trudgian, Updating the error term in the prime number theorem, Ramanujan J. 39 (2016), no. 2, 225–234. MR 3448979, DOI https://doi.org/10.1007/s11139-014-9656-6

Retrieve articles in Mathematics of Computation with MSC (2020): 11N05, 11N56, 11M06

Retrieve articles in all journals with MSC (2020): 11N05, 11N56, 11M06

David J. Platt
Affiliation: School of Mathematics, University of Bristol, Bristol, United Kingdom
MR Author ID: 1045993
Email: [email protected]

Timothy S. Trudgian
Affiliation: School of Science, The University of New South Wales Canberra, Australia
MR Author ID: 909247
Email: [email protected]

Keywords: Prime number theorem, zero-density estimate, explicit bounds
Received by editor(s): November 18, 2018
Received by editor(s) in revised form: November 12, 2019, and July 8, 2020
Published electronically: November 16, 2020
Additional Notes: The first author was supported by ARC Discovery Project DP160100932 and EPSRC Grant EP/K034383/1. The second author was supported by ARC Discovery Project DP160100932 and ARC Future Fellowship FT160100094.
Article copyright: © Copyright 2020 American Mathematical Society


JChau asked in a separate question if it's ever possible for the square root of a number to be negative, and another user moved for that to be closed as a duplicate of this one. It has since been deleted, but here is my answer to that other question, which is also pertinent here.

We say $x$ is a "square root" of $y$ if $x^2=y$. Thus, both 7$ and $-7$ are square roots of $49$.

However for positive reals $x$, by definition the square root function applied to $x$ yields the positive square root. Often one will abbreviate "the square root function applied to $x$" or equivalently "the positive square root of $x$" as simply "the square root of $x$," if no confusion should arise. Therefore we have $sqrt<49>=+7$, despite $-7$ also being a square root.

The square root function, like all bona fide functions, is single-valued rather than multi-valued, so if we were tasked with creating our own square root function from scratch we would have to make a choice between the two square roots of every positive number as the value the function takes if we want to further impose continuity (and, subsequently, smoothness for $x>0$), we would end up having to set $sqrt$ to either always be the positive square root or always the negative square root. At this point it's an understandable choice to make it always the positive one.

The same kind of "having to make a choice" situation arises if one wants to define a square root function for complex numbers. We can no long impose the same kind of continuity conditions and get a straight answer - instead we have to form a sort of "barricade" in which the value of the square root jumps dramatically when we cross over this barricade. This is known as a branch cut.

The standard branch in $Bbb C$ is where we consider the negative real axis as part of the quadrant above it but not part of the quadrant below it. In this setting, complex numbers when written in polar coordinates will have a phase (angle) in the interval $(-pi,pi]$ (note if you cross over the negative real axis, the phase will jump from one side of this interval to the other).

The standard branch normally comes up in the discussion of the logarithm, but it is connected to taking powers with complex numbers because $z^w:=exp(wln z)$ for complex $w,zinBbb C$ ($z e0$). The logarithm will be defined by $ln (re^)=(ln r)+i heta$, so the imaginary part of a logarithm will depend on which branch we have chosen. The default choice, usually unspoken, is the standard branch.

Using the standard branch, we have $sqrt<>>=exp(frac<1><2>(ln r+i heta))=e^<2>ln r>e^=sqrte^$. Thus the phase of $sqrt$ will be in $(-pi/2,pi/2]$ for all $zinBbb Zsetminus0$. This precludes $sqrt$ from ever being a negative real number, or even to the left of the imaginary axis. However, other nonstandard choices of branch cuts can lead to $z^<1/2>$ taking values on the negative real axis.

Another word for $ln$ and $sqrt<>$ with the standard branch is the principal value.

The idea of branch cuts leads into more advanced complex analysis topics of monodromy (which pertains to "running around" a singularity, like crossing over the branch mentioned earlier) and also Riemann surfaces, which can be thought of as what we get when we refuse to cut the plane into branches and instead consider a function multi-valued and look at its graph (I am probably butchering that description though).


Numeracy

Basic number concepts and skills (numeracy) generally emerge before school entry. It is important to promote the development of these competencies in young children and to know the best learning methods, as these skills are often predictive of children’s future school achievement.

Mathematics Instruction for Preschoolers

University of California, Berkeley, USA

Introduction

Teaching mathematics to young children, prior to formal school entry, is not a new practice. In fact, early childhood mathematics education (ECME) has been around in various forms for hundreds of years. 1 What has altered over time are opinions related to why ECME is important, what mathematics education should accomplish, and how (or whether) mathematics instruction should be provided for such young audiences.

Subject and Research Context

A concern among many early childhood experts, including educators and researchers, is the recent trend toward the “downward extension of schooling” 2 such that curricula, and the corresponding focus on assessment scores that were formally reserved for school-aged children, are now being pushed to preschool levels. 3 The motivation behind this downward push of curriculum appears to be largely political, with an increasing emphasis on early success, improving test scores, and closing gaps among specific minority and socio-economic groups. 4

Despite the concern related to the downward extension of school-aged curricula in general, there are persuasive factors encouraging the presence of at least some type of mathematical instruction for preschoolers, or at least for some groups of preschoolers. As Ginsburg et al.point out, learning mathematics is “a ‘natural’ and developmentally appropriate activity for young children”, 1 and through their everyday interactions with the world, many children develop informal concepts about space, quantity, size, patterns, and operations. Unfortunately, not all children have the same opportunities to build these informal, yet foundational, concepts of mathematics in their day-to-day lives. Subsequently, and because equity is such an important aspect of mathematics education, ECME seems particularly important for children from marginalized groups, 3 such as special needs children, English-as-additional-language (EAL) learners, and children from low socio-economic status (SES), unstable, or neglectful homes. 4

Recent Research Results

Equity in education is one major argument for the presence of ECME, but intimately tied to equity is the aspect of helping young mathematical minds move from informal to formal concepts of mathematics, concepts that have names, principles and rules. Children’s developing mathematical concepts, often building on informal experiences, can be represented as learning trajectories 5 that highlight how specific mathematical skills can build upon preceding experiences and inform subsequent steps. For example, learning the names, order and quantities of the “intuitive numbers” 1-3, and recognizing these values as sets of objects, number words, and as parts of wholes (e.g., three can be made up of 2 and 1 or 1 + 1 + 1), can help children develop an understanding of simple operations. 6 “Mathematizing,” or providing appropriate mathematical experiences and enriching those experiences with mathematical vocabulary, can help connect children’s early and naturally occurring curiosities and observations about math to later concepts in school. 3 Researchers have found evidence to suggest very early mathematical reasoning, 1,6,7 and ECME can help children formalize early concepts, make connections among related concepts, and provide the vocabulary and symbol systems necessary for mathematical communication and translation (for an example, see Baroody’s paper 6 ).

ECME may be important for reasons beyond equity and mathematization. In an analysis of six longitudinal studies, Duncan et al. 8 found that children’s school-entry math skills predicated later academic performance more strongly than attentional, socioemotional or reading skills. Similarly, early difficulty with foundation mathematical concepts can have lasting effects as children progress through school. Given that math skills are so important for productive participation in the modern world (Platas L, unpublished data, 2006), 9 and that specific mathematical domains, such as algebra, can serve as a gatekeeper to higher education and career options, 10 early, equitable and appropriate mathematical experiences for all young children are of critical importance.


CEILING.MATH Function

The CEILING.MATH Function is categorized under Excel Math and Trigonometry functions Functions List of the most important Excel functions for financial analysts. This cheat sheet covers 100s of functions that are critical to know as an Excel analyst . it will return a number that is rounded up to the nearest integer or multiple of significance. The function was introduced in MS Excel 2013.

As a financial analyst Financial Analyst Job Description The financial analyst job description below gives a typical example of all the skills, education, and experience required to be hired for an analyst job at a bank, institution, or corporation. Perform financial forecasting, reporting, and operational metrics tracking, analyze financial data, create financial models , we can use the CEILING.MATH function in setting the pricing after currency conversion, discounts, etc. When preparing financial models, it helps us round up the numbers as per the requirement.

Formula

=CEILING.MATH(number, [significance], [mode])

The CEILING.MATH function uses the following arguments:

  1. Number (required argument) &ndash This is the value that we wish to round off.
  2. Significance (optional argument) &ndash This specifies the multiple of significance to round the supplied number to.

If we omit the argument, it takes the default value of 1. That is, it will round up to the nearest integer. Significance will ignore the arithmetic sign. Remember that by default, the significance argument is +1 for positive numbers and -1 for negative numbers.

  1. Mode (optional argument) &ndash This will reverse the direction of rounding for negative numbers only.
    • If the mode argument is equal to zero, negative numbers are rounded up towards zero.
    • If the mode argument is equal to any other numeric value, negative numbers are rounded up away from zero.

How to use the CEILING.MATH Function in Excel?

To understand the uses of the CEILING.MATH function, let&rsquos consider a few examples:

Example 1

Let&rsquos see the results from the function when we provide the following data:

Number (argument)Significance (argument)ModeResultRemarks
210.67 211As the [significance] argument is omitted, it takes on the default value of 1.
103112The function rounds up to nearest multiple of 3. Even though mode is 1 but as the number is positive, the mode argument will not affect the result.
32.250.1 32.3It rounded up away from zero.
-32.25-11-33It rounds -32.25 down (away from 0) to the nearest integer that is a multiple of 1 with a mode of 1, which reverses rounding direction away from zero.
450100 500It rounded up to the nearest multiple of 100.
$5.371 6It rounded up to the nearest multiple of 6.

The formula used and results in MS Excel are shown in the screenshot below:

Example 2

Suppose we wish to know how many containers we will need to hold a given number of items. The data given to us is shown below:

The items per container indicate the number of items that can be held in a container.

The formula we will use is =CEILING.MATH(A2,B2). It rounds up A2 to the nearest multiple of B2 (that is items per container). The value derived will then be divided by the number of containers. For example, in the second row, =CEILING.MATH(385,24)/24, 385 will be rounded to a multiple of 24 and the result will be divided by 24.

A few notes about the CEILING.MATH Function

  1. #VALUE error &ndash Occurs when any of the arguments is non-numeric.
  2. Instead of the CEILING.MATH function, we can use the FLOOR.MATH function to round down to the nearest integer or significant figure. We can also use the MROUND function to round to a desired multiple or the ROUND function to round to a specified number of digits.
  3. CEILING.MATH is actually a combination of the CEILING function and the CEILING.PRECISE function.

Additional resources

Thanks for reading CFI&rsquos guide to important Excel functions! By taking the time to learn and master these functions, you&rsquoll significantly speed up your financial analysis. To learn more, check out these additional CFI resources:

  • Excel Functions for Finance Excel for Finance This Excel for Finance guide will teach the top 10 formulas and functions you must know to be a great financial analyst in Excel. This guide has examples, screenshots and step by step instructions. In the end, download the free Excel template that includes all the finance functions covered in the tutorial
  • Advanced Excel Formulas You Must Know Advanced Excel Formulas Must Know These advanced Excel formulas are critical to know and will take your financial analysis skills to the next level. Download our free Excel ebook!
  • Excel Shortcuts for PC and Mac Excel Shortcuts PC Mac Excel Shortcuts - List of the most important & common MS Excel shortcuts for PC & Mac users, finance, accounting professions. Keyboard shortcuts speed up your modeling skills and save time. Learn editing, formatting, navigation, ribbon, paste special, data manipulation, formula and cell editing, and other shortucts

Free Excel Tutorial

To master the art of Excel, check out CFI&rsquos FREE Excel Crash Course, which teaches you how to become an Excel power user. Learn the most important formulas, functions, and shortcuts to become confident in your financial analysis.