Barekeng: Journal of Mathematics and Its Applications is one of the scientific journals that publishes articles from research papers, literature studies, review articles, and problem-solving in Mathematics about Pure Mathematics and Applied Mathematics, as follows:

 Pure Mathematics

• Analysis

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. Analysis is a fundamental tool in pure mathematics, providing the theoretical foundation for many other areas of study. The ideas of this research on related topics can be traced to the works of Sotiris Ntouyas, S. Gähler,  Juan J. Nieto,  Yeol-Je Cho, and published books in Springer or other publishers.

• Algebra & Number Theory

Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication. While Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. The ideas of this research on related topics can be traced to the works of Alexander Zimmerman, Bijan Davvas, Jürgen Ü. Herzog, Kenneth R. Goodearl, Yong Zhang and published books in Springer or other publishers.

• Geometry & Topology

Geometry and topology are branches of pure mathematics that constitute a highly active area of central importance in the current mathematical landscape. Geometry is the branch of mathematics that deals with shapes, angles, dimensions and sizes of a variety of things we see in everyday life. While, Topology studies properties of spaces that are invariant under any continuous deformation. The ideas of this research on related topics can be traced to the works of Phillip A. Griffiths, Mark L. Green, Ljubisa D. R. Kočinac and published books in Springer or other publishers.

• Combinatorics,

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results and certain properties of finite structures. There are some approaches and subfield of combinatorics, such as: Enumerative combinatorics, Analytic combinatorics, Partition theory, Graph theory, Design theory, Finite geometry, Order theory, Matroid theory, Extremal combinatorics, Probabilistic combinatorics, Algebraic combinatorics, Combinatorics on words, Geometric combinatorics, Topological combinatorics, Arithmetic combinatorics, Infinitary combinatorics, etc. The ideas of this research on related topics can be traced to the works of Philippe Flajolet, Joseph A. Gallian, Mirka Miller, Martin Bača, and published books in Springer or other publishers.

 

 Applied Mathematics

• Numerical Analysis,

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis is a branch of mathematics that solves continuous problems using numeric approximation. It involves designing methods that give approximate but accurate numeric solutions, which is useful in cases where the exact solution is impossible or prohibitively expensive to calculate. There are some sub field of Numerical Analysis, such as: Computing values of functions; Interpolation, extrapolation, and regression; Solving equations and systems of equations; solving eigenvalue or singular value problems; optimization; evaluating integrals; differential equations. The ideas of this research on related topics can be traced to the works of Richard L. Burden and J. Douglas Faires, Kendall E. Atkinson. 

• Control & Optimization,

Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research.  There is some areas related to control, like linear quadratic control, the Hamiltonian system, Pontryagin’s maximum principle, discrete-time optimal control, etc. While, Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization.  There are some major subfields related to optimization, such as: Convex programming (Linear programming, Second-order cone programming, Semidefinite programming, Conic programming, Geometric programming); Integer programming; Quadratic programming; Fractional programming; Nonlinear programming; Stochastic programming; Robust optimization; Combinatorial optimization; Stochastic optimization; Infinite-dimensional optimization; Constraint satisfaction; etc. The ideas of this research on related topics can be traced to the works of Eduardo D. Sontag, Donald E. Kirk, Dimitri P. Bertsekas, Jhon R. Birge and Francois Louveaux.

• Artificial Neural Networks,

An Artificial Neural Network (ANN) is a machine-learning model inspired by the human brain's neural structure. It comprises interconnected nodes (neurons) organized into layers. Data flows through these nodes, adjusting the weights of connections to learn patterns and make predictions or An artificial neural network (ANN) combines biological principles with advanced statistics to solve problems in domains such as pattern recognition and game-play. ANNs adopt the basic model of neuron analogues connected to each other in a variety of ways. There are some topic related to ANN, such as: Feed-forward neural networks, Recurrent neural networks (RNNs), Convolutional neural networks (CNNs), Deconvolutional neural networks, Modular neural networks, etc. The ideas of this research on related topics can be traced to the works of Laurene V. Fauset, Simon Haykin, and Charu C. Aggarwal.

• Fuzzy

Fuzzy mathematics is the branch of mathematics including fuzzy set theory and fuzzy logic that deals with partial inclusion of elements in a set on a spectrum, as opposed to simple binary "yes" or "no" (0 or 1) inclusion. Fuzzy mathematics is essentially a discipline which recognizes that boundaries are inexact, and fuzzy clustering therefore proceeds by recognizing explicitly that cluster membership is probabilistic rather than deterministic. The ideas of this research on related topics can be traced to the works of Jerry Mendel and Robert Jhon, Bart Kosko, Oscar Cordon and Francisco Herrera, Chih-Fong Tsai, Serafin Moral and Alberto Cano.

• Mathematics Modelling & Simulation,

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The ideas of this research on related topics can be traced to the works of Kai Velten; Frank R. Giordano, Maurice D. Weir and William P. Fox; Clive L. Dym; Edward A. Bender; and Charles R. Hadlock.

• Computational Mathematics,

Computational Math is a specialised field that combines mathematical theory, practical engineering, and computer science or Computational mathematics is the study of the interaction between mathematics and calculations done by a computer. A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. The ideas of this research on related topics can be traced to the works of Robert E. White; and Randall J. LeVeque.

• Applied Statistics & Probability,

Probability And Statistics are the two important concepts in Maths. Probability is all about chance. Whereas statistics is more about how we handle various data using different techniques. It helps to represent complicated data in a very easy and understandable way. Applied Statistics includes planning for the collection of data, managing data, analyzing, interpreting and drawing conclusions from data, and identifying problems, solutions and opportunities using the analysis. The ideas of this research on related topics can be traced to the works of Ming Yuan; Andrew Gelman; Patrick and Royston.

• Ethno-Mathematics,

Ethnomathematics is the study of the relationship between mathematics and culture. In a deeper understanding, ethnomathematics refers to mathematics which is practiced by members of a cultural group who share similar experiences and practices with the mathematics that can be in a unique form. Culture gives diverse and interesting contexts in mathematics learning to be discussed. Therefore, the scope of ethnomathematics is an important part of the focus and scope of the journal. The ideas of this research on related topics can be traced to the works of Marcia Ascher, Ubiratan d'Ambrosio, Robert Ascher, Marcelo C. Borba, and published books in Springer, Taylor & Francis, or other publishers. The ideas of this research on related topics can be traced to the works of Marcia Ascher, Ubiratan d'Ambrosio, Robert Ascher, Marcelo C. Borba, and published books in Springer, Taylor & Francis, or other publishers

• Bio-Mathematics,

Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and practical research. The field of biomathematics, sometimes also called mathematical or theoretical biology, is an interdisciplinary field of scientific research which aims to address questions which arise from biological systems using appropriate mathematical and computational theory. The ideas of this research on related topics can be traced to the works of Leah Edelstein-Keshet; Hiroaki Kitano and Bernhard Palsson; Sir Ronald Ross, W. O. Kermack, and A. G. McKendrick.

• Pattern Recognition,

Pattern recognition is an important component in mathematics learning; it supports both conceptual learning and procedural fluency. Pattern recognition is the process of recognizing patterns by using a machine learning algorithm. Pattern recognition is the process of recognizing patterns by using a machine learning algorithm. Pattern recognition can be defined as the classification of data based on knowledge already gained or on statistical information extracted from patterns and/or their representation. One of the important aspects of pattern recognition is its application potential. The ideas of this research on related topics can be traced to the works of Christopher M. Bishop; Sepp Hochreiter and Jurgen Schmidhuber.

• Dynamical Systems

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. The ideas of this research on related topics can be traced to the works of Steven H. Strogatz; Morris W. Hirsch, Stephen Smale and Robert L. Devaney.

It cordially contributions from the researcher, lecturer, and teacher of related disciplines. The language used in this journal is English.