Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

It is a collection of functions for describing an object. Mostly calculus and some additionals like infinite serie etc. Geometry and trigeometry now are out of place. Wherever real or complex functions or algorthims are detected it ist mathematical analysis.

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According to Wikipedia, Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

According to Encyclopedia Mathematics, Mathematical analysis

is the part of mathematics in which functions (cf. Function) and their generalizations are studied by the method of limits (cf. Limit). The concept of limit is closely connected with that of an infinitesimal quantity, therefore it could be said that mathematical analysis studies functions and their generalizations by infinitesimal methods.

The name "mathematical analysis" is a short version of the old name of this part of mathematics, "infinitesimal analysis"; the latter more fully describes the content, but even it is an abbreviation (the name "analysis by means of infinitesimals" would characterize the subject more precisely). In classical mathematical analysis the objects of study (analysis) were first and foremost functions. "First and foremost" because the development of mathematical analysis has led to the possibility of studying, by its methods, forms more complicated than functions: functionals, operators, etc.

Everywhere in nature and technology one meets motions and processes which are characterized by functions; the laws of natural phenomena also are usually described by functions. Hence the objective importance of mathematical analysis as a means of studying functions.

Mathematical analysis, in the broad sense of the term, includes a very large part of mathematics. It includes differential calculus; integral calculus; the theory of functions of a real variable (cf. Functions of a real variable, theory of); the theory of functions of a complex variable (cf. Functions of a complex variable, theory of); approximation theory; the theory of ordinary differential equations (cf. Differential equation, ordinary); the theory of partial differential equations (cf. Differential equation, partial); the theory of integral equations (cf. Integral equation); differential geometry; variational calculus; functional analysis; harmonic analysis; and certain other mathematical disciplines. Modern number theory and probability theory use and develop methods of mathematical analysis.

Nevertheless, the term "mathematical analysis" is often used as a name for the foundations of mathematical analysis, which unifies the theory of real numbers (cf. Real number), the theory of limits, the theory of series, differential and integral calculus, and their immediate applications such as the theory of maxima and minima, the theory of implicit functions (cf. Implicit function), Fourier series, and Fourier integrals (cf. Fourier integral).

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

Dear Friends,

thank you for your comments on definition of Mathematical analysis. My question is definition of mathematical analytics.

I don't think there is an accepted definition of mathematical analytics.

One, for example finds this:

" We find patterns and derive insights by visually exploring data. Predictive and prescriptive analytics supports better decisions and smarter data based-actions. Including big data-enabled algorithms. " (https://enyanalytics.com/drill_service/mathematical-analytics/)

Analytics seems to be a synonim for (big) data analysis.

The book Analytics in a Big Data World by Bart Baesens describes "The Analytics Process Model" as "understanding what data is needed for the application, data selection, data cleaning, data transformation, analytics (patterns), interpretation and evaluation".

Dear Dr.

Zhaohao Sun

Greating!

Mathematical Analytics and Operations Research addresses a critical need in business for scientifically-trained analysts who can use mathematical models to interpret big data, analyze markets and forecast trends—this major is ideally suited to students with an interest in business or economics.

The Mathematical Analytics and Operations Research major provides training for students planning careers in any field that requires mathematical methods. For example: the discovery of meaningful patterns in high-dimensional data; scientific approach for making decisions based on models that optimize the decision parameters such as cost, time-to-completion, transportation logistics, scheduling of tasks, etc.; data visualization to communicate and present decisions to others. Graduates of our program will distinguish themselves for their problem-solving skills, computational and modeling ability, and excellent communication skills. These abilities allow them to pursue scientific or technical careers in industry, education, or government. In addition, their strong analytic skills prepare them well to continue with graduate education or to participate in research and development, and other creative and innovative efforts in science, arts and humanities, engineering, and business.

Upon graduation, Mathematical Analytics and Operations Research majors should have a set of fundamental competencies:

Mathematical Analytics and Operations Research addresses a critical need in business for scientifically-trained analysts who can use mathematical models to interpret big data, analyze markets and forecast trends—this major is ideally suited to students with an interest in business or economics. Students will develop the skills to perform data analysis and develop reliable models for forecasting, decision-making and long-term planning in fields ranging from financing to entertainment and education.

Real World Outcomes: 

Careers in this field can be found in virtually every industry, and employment growth for operations research analysts is expected to exceed the average for all occupations. Graduates may also choose to continue with postgraduate work in areas such as Economics, Applied Mathematics, Operations Research, Financial Engineering, and Management Science, or pursue an professional degree for higher-level career opportunities. Management and analysis of big data is at the core of decision-making processes for a wide variety of industries. Corporations, governments, relief agencies, technology companies, social media platforms, websites and organizations of all types use analytics in guiding daily and long-range decisions.

It is my pleasure to help you, you can read the following links

https://ucdavis.pubs.curricunet.com/Catalog/mathematical-analytics-operations-research

https://en.wikipedia.org/wiki/Mathematical_analysis

https://www.encyclopediaofmath.org/index.php/Mathematical_analysis

https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/m/Mathematical_analysis.htm

https://en.wikiquote.org/wiki/Mathematical_analysis

https://maths-people.anu.edu.au/~john/Assets/Lecture%20Notes/B21H_97.pdf

https://www.researchgate.net/deref/https%3A%2F%2Fenyanalytics.com%2Fdrill_service%2Fmathematical-analytics%2F

With best wishes.

https://www.ucdavis.edu/majors/mathematical-analytics-and-operations-research/