### i-manager's Journal on Mathematics (JMAT)

Article

#### Abstract

In this article, the author has discussed the various areas of recreational mathematics which was interesting and makes fun. The recreational mathematics includes mathematical puzzles, mathematical games, mathematical Riddles, Brain games, number Pattern, magic squares, birthday Magic Square, paradoxes and unsolved problems which are discussed in this article. Recreational mathematics is an umbrella term for mathematics carried out for recreation including self-education and entertainment rather than a strictly research and application-based professional activity, although it is not necessarily limited to being an endeavour for amateurs. It often involves mathematical puzzles and games. Recreational mathematics is a treasury of problems which make mathematics fun. Mathematical games are multiplayer games whose rules, strategies, and outcomes can be studied and explained using mathematics. A game or toy in which you have to fit into separate pieces together, or a problem or question that you have to answer by using your skill or knowledge. Mathematical puzzles require mathematics in order to solve them. A riddle is a statement or a question or phrase having a double or veiled meaning, put forth as a puzzle to be solved. Brain games are a quick and easy way to practise your literacy and numeracy skills. A pattern constitutes a set of numbers or objects in which all the members are related with each other by a specific rule. These are the areas of recreational mathematics and it inspire the learners to learn mathematics as well as to solve the problems.

Research Paper

#### Abstract

This monograph provides an epistemological rational for the novel “Multiple Trichotomous Coefficient of Variation Analysis” statistic represented by the acronym [“MULTICOVA”]. This new statistic is an innovative in–depth way of further investigating a statistically significant post hoc Tri–Squared Test. MULTICOVA is an advanced and detailed statistical procedure for the internal testing of the outcomes of the mixed methods Tri–Squared Test (first introduced in the Journal on Mathematics, and detailed further in the Journal on Educational Technology, Journal on School Educational Technology, and in the Journal on Educational Psychology). MULTICOVA is an advanced statistical procedure; which is designed to measure the “Trichotomous Coefficient of Variation” of inputted and outputted Tri–Squared variables. The Trichotomous Coefficient of Variation is also a normalized measure of a trichotomous probability distribution or trichotomous frequency distribution. This new statistic is an innovative approach to the sequential series of advanced post hoc Tri–Squared Test statistical metrics. Multiple MULTICOVA equations are presented, as well as the entire process of advanced statistical Trichotomous Coefficient of Variation analytics that illustrate how to conduct this particular method of inquiry.

Research Paper

#### Abstract

Chemical and Soret effects on Unsteady MHD (Magnetohydrodynamics) free convective flow of an incompressible, dissipative fluid flow past an accelerated vertical plate in presence of inclined magnetic field through porous medium is investigated under Joule effect. The main aim of the present paper is to investigate unsteady MHD free convection boundary layer flow of a Newtonian fluid with chemical and Soret effects on flow past an accelerated vertical plate in presence of inclined magnetic field with joule effect. The governing partial differential equations have been solved numerically; using finite difference technique. The numerical solutions are obtained for the velocity, temperature, and concentration distributions. The effects of system parameters, such as the Chemical reaction, Soret number, thermal Grashoff number, modified Grashoff number, Eckert number, Angle of inclination and magnetic field parameter on the flow fields are thoroughly presented through graphs and tables. Here it is observed that the velocity increases with the thermal, modified Grashoff numbers and with Eckert number. The temperature distribution increases with the increase of Eckert number and the heat absorption, whereas for high radiation and with the increase of thermal and modified Grashoff numbers, temperature decrease is observed. With the increase of the chemical reaction parameter, Schmidt number, Soret number, Eckert number and time ,the concentration distribution decrease is observed.

Research Paper

#### Abstract

Viscous dissipation effects on the unsteady natural convective flow past a parabolic starting motion of the infinite vertical plate with variable temperature and variable mass diffusion is investigated. The plate temperature and the concentration level near the plate are raised linearly with time. The dimensionless governing unsteady, non-linear, coupled partial equations are solved by using the unconditionally stable explicit finite difference method of DuFort – Frankel's type. The effect of velocity profiles are studied for different physical parameters like Eckert number, Prandtl number, thermal Grashof number, mass Grashof number, Schmidt number, and time. It is observed that the velocity increases as the value of the thermal Grashof number or mass Grashof number increase. The trend is just reversed with respect to the Schmidt number.

Review Paper

#### Abstract

The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field. This paper examines the discrimination they faced and how they overcame this discrimination, as well as the contributions they have made to the mathematics field. In addition, studies about the effects of gender on mathematics achievement were explored and recognized trends and changes in favor of women in the mathematics field in recent years. This paper also reviews Bhaskaracharya's classic work Lilavati. The author wrote on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, geography, and the mathematical techniques and astronomical equipment used in these studies. Bhaskara II was also a noted astrologer, and traditionally he has named his first work, Lilavati, after his daughter. This note is a kind of review article based on references cited at the end of this paper.