Algebra 2 Lopez

[Brook Mithani]

Iam a third year PhD student at Texas A and M University in the Department of Mathematics.

My research interests lie in geometry ---> geometric PDEs, geometric microlocal analysis, low-dimensional topology, gauge theory and string theory ---> I think of problems in the (many) Floer theories, gauge theory PDEs (e.g., Yang-Mills, Seiberg-Witten, Bogomolny, Hitchin, Nahm's, Kapustin-Witten), and homological mirror symmetry. My advisors are Prof. Dean Baskin and Prof. Chris Pope.

One of my goals in life is to make high-level math reachable and understandable to a wider group of peoplethan the one today. I want to teach these ideas in such a way that anyone, willingly, can understand them. It is common to hear that mathematics is very hard, or among the least liked subjects in school. However, this could be due to inadequate teaching, or lack of knowledge about the material.Hence, the history of mathematics can also be changed through teaching. I have been surrounded with academia for the most part of my life. Thus, I am a firm believer that education is a door where students can start pursuing great things, actually enjoying going to class, and regain hope in the things to come.

In my Master's, I was given some interesting problems. I believe is against the University policy to upload them on the internet.But they follow closely the books above. I have solutions to some selected exercises from my time in ISU:ODEs by Perko, PMA by Rudin, Linear algebra by Prof. Hogben, and Intro Algebra by Hungerford. I am pending to upload them.

Professor Lpez researches connections of commutative algebra, like vanishing ideals and Grbner basis, with the fundamentals of coding theory and its applications, including quantum error correction, coding for post-quantum cryptography, and distributed storage systems.

More specifically. A linear code, or just a code, is the main object studied in coding theory. For any given code, it is possible to attach an algebraic object, so the properties of the code are studied using tools from commutative algebra, algebraic geometry, or combinatorics. This bridge allows us to construct families of codes with specific properties to satisfy the most demanding and particular technological needs.

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The college asked the math department to design courses tailored to those students, starting with its welding, culinary arts and criminal justice programs. The first of those, math for welders, rolled out in 2013.

Stone explained how math in context works. Students start with a practical problem and learn a math principle for solving it. Next, they use the principle to solve a similar practical problem, to see that it applies generally. Finally, they apply the principle on paper, in say, a standardized test.

Meanwhile, Algebra I was a huge barrier for many Rogue students. About a third of those taking the course or a lower-level math course failed or withdrew. That meant they had to retake the class and likely stay another term to graduate; since many were older students with families and obligations, hundreds dropped out, school administrators said.

So, in 2010, Gardner applied for and got a National Science Foundation grant to create two new applied algebra courses. Instead of abstract formulas, students would learn practical ones: how to calculate the volume of a wheelbarrow of gravel and the number of wheelbarrows needed to cover an area, or how much a beam of a certain size and type will bend under a certain load.

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Through the years, much of the research at the CRA has been focused on modifications of the notions of projectivy and injectivity. Recently, Lpez has introduced an alternative perspective by studying notions (labeled poor modules) that are the opposite of projectivity and injectivity. His work (in collaboration with doctoral students and postdoctoral visitors) has yielded various types of associated ordered structures (which they have named profiles) for every ring. The study of these various profiles aims at shedding light on the algebraic properties of the rings themselves.

The Ohio University Center of Ring Theory and its Applications was founded in 2001 by Lpez and Distinguished Professor Emeritus Surender K. Jain. Jain served as director of the CRA until his retirement in 2009, at which time Lpez became director. The CRA has been a magnet for mathematical activity at Ohio University. The center frequently hosts speakers and holds short-courses on specialized subjects. In this way, Athens has been visited by many leading mathematicians in the past, including Fields Medalist Efim Zelmanov. (The Fields medal is considered the equivalent of the Nobel Prize in Mathematics.) The CRA is also a destination point for mathematicians to visit during sabbatical leaves and for young post-docs to receive mentoring and training during the early years of their careers.

One of the first projects of the CRA was to establish the Journal of Algebra and its Applications (JAA). With Jain and Lpez as executive editors, JAA is completing its 11th year and is widely regarded one of the leading journals in the field of Algebra. Lpez is a member of various other editorial boards; his membership in Advances in Mathematics of Communication is testimony to his activity in Coding Theory. Recently, he was appointed to the editorial board of the So Paulo Journal of Mathematical Sciences. Universidade de Sao Paulo is consistently ranked the top university in Latin America.

This course is designed to allow students to investigate the concepts of deductive and inductive logic and the analytical process of problem solving through group work, computer activity, and class projects. Students are taught to develop clear, logical methods of thinking and proofs. Some of the key topics covered are: triangles, quadrilaterals, circles, and deductive proofs.

This course is designed to allow students to investigate the concepts of deductive and inductive logic and the analytical process of problem-solving through group work, computer activity, and class projects with higher expectations of proficiency. Honors Geometry students should be highly motivated and self-driven. Some of the key topics covered are: triangles, quadrilaterals, circles, and deductive proofs. Students are taught to develop clear, logical methods of thinking and proofs.

This course is an accelerated Algebra 2 course, covering advanced topics of algebra and a full course in functional trigonometry. The use of technology in problem-solving and applications is strongly emphasized.

This course delves into limits as they connect to the differentiation of algebraic and transcendental functions, the concept of derivatives, and their connection to rates of change. It also covers differentiation to solve related rate and optimization problems and computing definite and indefinite integrals. This course will focus on real-world applications of calculus across the curriculum from STEM to Business and Economics.

The first semester of this course will explore analytical trigonometric topics. The second semester will include the study of advanced algebra topics such as: functional and graphical analysis, vector analysis, matrices, sequences, and conics Sections. This is the non-honors equivalent of Honors Precalculus and will not provide entrance into AP Calculus AB.

The Business Accounting and Personal Finance curriculum focuses on the individual student and the ways they use math in their daily lives. This course is designed for students who have successfully completed Algebra 2 and want to continue their study of mathematics in a class that is challenging and applicable to their everyday lives. The course will cover the stock market, business management, banking, credit, automobile ownership, employment, taxes, independent living, retirement and budgeting. Students will apply mathematics concepts that span from algebra, geometry and statistics. This course will encourage students to establish career goals that will provide adequate income and personal fulfillment, give them the skills they need to understand personal financial planning and money management skills and understand the personal and societal consequences of financial decisions.

A challenging course of advanced topics: the study of advanced algebra, analytic trigonometry, conic sections, sequences and Series, and limits are covered in depth. The use of technology in problem-solving and applications is strongly emphasized. This course provides entry to AP Calculus AB.

This course is a college-level course only offered to our most proficient students who have demonstrated a higher level of proficiencies in mathematics. The course material is challenging, covering differential and integral calculus including inverse functions, slope fields, Solids of revolution, differential equations, and applications of derivatives and integrals. Taking the Advanced Placement exam is optional.

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