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{{Short description|Practical mathematics used in business}}
{{more footnotes|date=January 2018}}'''Business mathematics''' are [[mathematics]] used by [[Commerce|commercial]] enterprises to record and manage business operations. Commercial organizations use mathematics in [[accounting]], [[Field inventory management|inventory management]], [[marketing]], sales [[forecasting]], and [[financial analysis]].<ref name="Olivier">J. Olivier (2021). [https://math.libretexts.org/Bookshelves/Applied_Mathematics/Business_Math_(Olivier) Business Math: A Step-by-Step Handbook]. [[Lyryx Learning]] ([[open textbook]])</ref>

Mathematics typically used in commerce includes [[elementary arithmetic]], [[elementary algebra]], [[statistics]] and [[probability]]. For some management problems, more advanced mathematics - [[calculus]], [[Matrix (mathematics)#Basic operations|matrix algebra]], and [[linear programming]] - may be applied.

==High school==
''Business mathematics,'' sometimes called ''commercial math'' or ''consumer math'', is a group of practical subjects used in [[commerce]] and everyday life. In schools, these subjects are often taught to students who are not planning a university education. In the United States, they are typically offered in [[high schools]] and in schools that grant [[associate's degrees]]; elsewhere they may be included under [[business studies]]. These courses often fulfill [[Secondary education in the United States#Core|the general math credit]] for high school students.<ref name="consumer math"/>

The emphasis in these courses is on computational skills and their practical application, with practice being predominant. A (U.S.) business math course typically <ref name="consumer math">[https://www.consumermath.org/for-the-student/student-consumer-math-curriculum/ Student Consumer Math Curriculum ], consumermath.org</ref> includes a review of [[elementary arithmetic]], including [[fractions]], [[decimals]], and [[percentages]]; elementary [[algebra]] is included also. The practical applications of these techniques include [[revenues]], [[checking accounts]], [[discounts and allowances|price discounts]], [[markup (business)|markups]], [[payroll]] calculations, [[interest|simple and compound interest]], [[credit (finance)|consumer and business credit]], and [[mortgages]].

==University level==
===Undergraduate===
''Business mathematics'' comprises mathematics [[Course credit|credits]] taken at an [[undergraduate]] level by [[Business education#Undergraduate education|business students]].
The course <ref>See, for example, this [[DSST (standardized test)|DSST]] course outline: [https://www.getcollegecredit.com/wp-content/assets/factsheets/BusinessMathematics.pdf Business Mathematics Exam Information]</ref> is often organized around the various [[Outline of business management#Areas of management application|business sub-disciplines]], including the above applications, and usually includes a separate module on [[time value of money|interest calculations]]; the mathematics itself comprises mainly [[Elementary algebra#Solving algebraic equations|algebraic techniques]].<ref name="Olivier"/>
Many programs, as mentioned, extend to more sophisticated mathematics.
Common credits are ''Business Calculus''
<ref>Two [[open textbook|open texts]] are:
*Shana Calaway, Dale Hoffman, David Lippman (2013). [http://www.opentextbookstore.com/buscalc/buscalc/index.php ''Business Calculus''], OpenTextBookStore
*Mike May, Anneke Bart (2013). [https://mathstat.slu.edu/~may/ExcelCalculus/ExcelCalculus.html ''Business Calculus with Excel''], [[Saint Louis University]]</ref>
and ''[[business statistics|Business Statistics]]''.<ref>Two [[open textbook]]s are:
*Holmes, L., Illowsky, B., Dean, S (2017). [https://open.umn.edu/opentextbooks/textbooks/509 ''Introductory Business Statistics'']
*Nica, M. (2013). [https://open.umn.edu/opentextbooks/textbooks/384 ''Principles of Business Statistics'']
</ref>
Programs may also cover matrix operations, as above.
At many US universities, business students (instead) study "[[finite mathematics]]",<ref>An open text is Rupinder Sekhon (2011). [https://open.umn.edu/opentextbooks/textbooks/396 ''Applied Finite Mathematics''].</ref>
a course combining several applicable topics, including basic probability theory, an introduction to linear programming, some theory of matrices, and introductory [[game theory]]; the course sometimes includes a high level treatment of calculus.

Since these courses are focused on problems from the business world, the syllabus is then adjusted re [[Mathematics education#Content and age levels|standard courses]] in the mathematics or science fields.<ref name="difference">[https://www.mathbootcamps.com/what-is-the-difference-between-business-calculus-and-calculus/ What is the difference between business calculus and calculus?]</ref>
The calculus course especially emphasizes [[Derivative|differentiation]], leading to [[Profit maximization|optimization of costs and revenue]].
[[Integral|Integration]] is less emphasized, as its business applications are fewer
— used here <ref>See, e.g.: [http://www2.gcc.edu/dept/math/faculty/BancroftED/buscalc/chapter3/section3-7.php The Integral § Applications to Business]; [https://mathstat.slu.edu/~may/ExcelCalculus/sec-7-7-InvestmentDepreciation.html Applications of the integral: Investment and depreciation]; [https://www.math24.net/applications-integrals-economics Applications of Integrals in Economics]</ref> [[continuous compounding|in some interest calculations]], and for (theoretically) [[Cost curve|aggregating costs]] and / or [[Total revenue|revenue]]
— and it is more technically demanding.
Relatedly, in a regular calculus course students study [[trigonometric functions]], whereas courses here do not typically cover this area. As regards formal theory, as these are applied courses, very few [[proof (mathematics)|proofs or derivations]] are included, unlike standard courses.<ref name="difference"/>
(Although see [[Bachelor of Science in Business Administration]] and [[Bachelor of Business Science]].)
The statistics syllabus, similarly of an applied nature, is described [[Business statistics|under that article]].

Note that [[Bachelor of Economics|economics majors]], especially those planning to pursue [[Master of Economics|graduate study in the field]], are encouraged to instead take regular calculus, as well as [[linear algebra]] and other advanced math courses, especially [[real analysis]]. Some economics programs (instead) include a module in "mathematics for economists",<ref name="Eyal"/> providing a bridge between the above "Business Mathematics" courses and [[mathematical economics]] and [[econometrics]].
Programs in [[management accounting]], [[operations management]], [[risk management]] and [[credit management]], may similarly include supplementary coursework in relevant quantitative techniques, generally [[Linear regression|regression]], and often linear programming as above, as well as other optimization techniques and various probability topics.
<ref>See for example the "Qualification Subject" [https://www.icm.education/subjects/quantitative-methods-for-managers Quantitative Methods For Managers] offered by the [[Institute of Commercial Management]].</ref>

===Postgraduate===
[[Business education#Postgraduate education|At the postgraduate level]], ''generalist'' management and finance programs include quantitative topics which are foundational for the study in question - often exempting students with an appropriate background. These are usually "interest mathematics" and statistics, both at the above level. [[MBA]] programs often also include basic [[operations research]] (linear programming, as above) with the emphasis on practice, and may combine the topics as "quantitative analysis"; [[master of science in finance|MSF programs]] may similarly cover applied / [[financial econometrics]].

More technical [[master's degree|Master's]] in these areas, such as those in [[management science]] and [[Master of Quantitative Finance|in quantitative finance]], will entail a deeper, more theoretical study of operations research and econometrics, and extend to further advanced topics such as [[mathematical programming]], [[Monte Carlo method]]s, and [[stochastic calculus]].
<ref>See e.g: Robert Hildebrand, ed. (2024). [https://github.com/open-optimization/open-optimization-or-book/tree/master ''Mathematical Programming and Operations Research''] (Open text)</ref>
<ref>See e.g: Arash Fahim (2019). [https://www.dbooks.org/introduction-to-financial-mathematics-5651614967/read/ ''Introduction to Financial Mathematics: Concepts and Computational Methods''] (Open text)</ref>
These programs, then, do not include or entail "Business mathematics" ''per se''.

Where [[mathematical economics]] is not a degree requirement, [[Master of Economics|graduate economics programs]] often include "quantitative techniques", which covers (applied) [[linear algebra]], [[multivariate calculus]], and [[mathematical optimization|optimization]], and may include [[dynamical systems]] and analysis;
<ref name="Eyal">Open texts include:
*Katherine Eyal (2014). [https://vula.uct.ac.za/access/content/group/95dfae58-9991-4317-8a1d-e2d58f80b3a3/Published%20OER%20UCT%20Resources/Mathematics%20for%20Economics/Home.htm ''Mathematics for Economists'']
*Frank Werner and Yuri Sotsko (2006). [https://library.oapen.org/handle/20.500.12657/24191 ''Mathematics of Economics and Business'']
*Bruno Belevan, ''et al.'' (2020). [https://nisha-malhotra.arts.ubc.ca/open-textbook/ ''Optimal, Integral, Likely'']
</ref>
regardless, econometrics is usually a separate course, and is dealt with in depth.
Similarly, [[Master of Financial Economics]] (and ''MSc'' Finance) programs often include a (supplementary) course covering the calculus, optimization, linear algebra, and probability techniques required for specific topics.

== See also ==
* [[Operations research]]
* [[Management science]]
* [[Econometrics]]


==References==
{{Reflist}}

==Bibliography==
* Anthony, M. & Biggs, N. (1996). ''Mathematics for Economics and Finance: Methods And Modelling,'' Cambridge University Press. {{ISBN| 9780521559133}}
* Bradley, Teresa (2013). ''Essential Mathematics for Economics and Business'' 4th Edition, Wiley. {{ISBN|978-1118358290}}
* Brechner, Robert. (2006). ''Contemporary Mathematics for Business and Consumers,'' Thomson South-Western. {{ISBN|0-324-30455-2}}
* Dowling, Edward (2009). ''[[Schaum's Outlines|Schaum's Outline]] of Mathematical Methods for Business and Economics,'' McGraw-Hill. {{ISBN|0071635327}}
* Rosser, M. & Lis, P. (2016). ''Basic Mathematics for Economists'' 3rd Edition. Routledge. {{ISBN|9780415485920}}
* Wegner, Trevor. (2016). ''Applied Business Statistics: Methods and Excel-Based Applications,'' Juta Academic. {{ISBN|9781485111931}}

[[Category:Mathematics education]]
[[Category:Business education]]

Business mathematics - Revision history

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