Modeling and not model for Math for all Purposes

0 %
100 %
Information about Modeling and not model for Math for all Purposes
Education

Published on July 20, 2018

Author: rms916A

Source: authorstream.com

Slide1: NA MA S TE Columbus College On Behalf of Nepal Mathematics Centre is pleased to welcome you all at NeMaCeL 1 New Baneswor, Sankhamol Road Friday October 8, 2010, 4.30 p.m . Slide3: Friends and Colleagues, Just One night before the Beginning of an Adventure In Mathematics (AIM) through Autumn-Mini-Math-Camp (AmiMaC), we are gathering here today at the premise of Columbus College. I would, first of all, like to thank the Columbus College Family for giving me this special opportunity to be present myself before you all. Please do accept my Slide4: NAMASTE gd:]t HjHjnkf President Nepal Mathematics Centre Nxf:;f]M km\ofkm'NhLM ;nfdflnsd Prof. Dr. R.M.Shreshtha Slide5: Friends and Colleagues, Exactly 18 months ago, I got a similar opportunity to deliver a talk among friends and colleagues in the next door campus - The Boston Campus. My lecture today is a slightly improved version so as to would reflect part of the content and extent of the Autumn- Mini-Math-Camp that is going to be held for 3 days starting from tomorrow. As our Camp is focusing on some special topics added to Grade XI mathematics course, I shall try to reflect those topics in my lecture today. Slide6: First Slide of the talk that I gave last time Slide7: Differentials and Differences Set Union and Intersection Secant approaches vertical tangent Secant and tangent Welcome To SEMINAR CUM WORKSHOP On Undergraduate Mathematics April 11- April 13 2009 Chaitra 29 – Chaitra 31 2065 ( Building Mathematical Foundation for Solid Waste Management Mathematics ) Slide9: Columbus College A Simple Mathematical Model of Solid Waste Generatio in KMC New Baneswor, Sankhamol Road Friday October 8, 2010, 4.30 p.m . Slide10: Country : Nepal Capital : Kathmandu City Area : Appro. 51 sq.km Estimated Population: 725000 (census 2001) Population growth: 6% p.a. Kathmandu at a Glance Waste Collection - Kathmandu: Waste Collection - Kathmandu KMC Road Side collection 175 ton/day Container collection 21 ton/day Total = 196 ton/day PSP Door to door 110 ton/day Total (KMC&PSP) = 306 ton/day % Collection 91% Uncollected waste (29 ton/day) 9% WASTE ARRIVAL GRAPHS: WASTE ARRIVAL GRAPHS A small sample from a big collection . Waste Sorting: Waste Sorting Four Categories: Four Categories Kathmandu's Waste: Kathmandu's Waste Source: KMC/JICA 2005 A COUPLE OF WASTE ARRIVAL GRAPHS: A COUPLE OF WASTE ARRIVAL GRAPHS Do the Waste Arrival Graphs look something like the bounding line along which Nepal hills and mountains touch the sky? Bhanjyngs/Mountain Passes !!!: Do the Waste Arrival Graphs look something like the bounding line along which Nepal hills and mountains touch the sky? Bhanjyngs/Mountain Passes !!! Slide23: As a student of mathematics, here is how I do observe the curve along which the hills and mountains appear to meet the sky. Slide24: A Typical Graph Slide28: Basic Building Blocks Basic Concepts Sets, Patterns and Logic Number Sense and Operations, Space,Time and Weight, Data and Data Processing Plus Pictorial and Graphical Representations Models Almost Everything from Pre-school to Grade 11 Level Mathematics Some Foundational Concepts Set relations and Algebra: Some Foundational Concepts Set relations and Algebra Slide30: W5 – W6 = { degradable waste } - { non-degradable waste }, = { degradable waste }. Note : 1 type – 1 type = 1 type. What a modern mathematics! 1 – 1 = 1? Sets as Bit-strings: Sets as Bit-strings W = { glass , iron , plastic, vegetable, wood } = 1 1 1 1 1 W3 = { glass , iron , vegetable } and W4 = { plastic, vegetable, wood }, W3 : 1 1 0 1 0 and W4 : 0 0 1 1 1 W3  W 4 = (W3 – W4 )  (W 4 – W3 ) = ({ glass , iron , vegetable } – { plastic, vegetable, wood })  ({ plastic, vegetable, wood }– { glass , iron , vegetable }) = { glass , iron , plastic, wood } Counting Principle: Counting Principle For any two sets W3 and W4, then n (W3  W4) = n (W3) + n (W4) - n (W3 ∩ W4 Note : 3 items from W3 + 3 items of W4 = 5 items in the whole. What a mathematics? This is what computer does. 3 + 3 = 5 Can you believe? Cartesian Product A  B = {(5, d), (5, n), (6, d), (6, n)}.: Cartesian Product A  B = {(5, d ), (5, n ), (6, d ), (6, n )}. Relation (0ne-many): Relation (0ne-many) Relation (Many-to-One): Relation (Many-to-One) Relation (One-One & Onto: Relation (One-One & Onto Slide38: For constructing a mathematically acceptable definition of function, we first have to see how we can (i) collect (ii) sort and classify/ group (iii) present in a tabular form, (iv) visualize graphically , and (v) examine the tendency of concentration or scattering of the data. Slide39: Once we have an idea how the data are distributed , we can then think , make supposition , argue logically , draw conclusion and derive rules or state laws that will help us construct or define a mathematically acceptable functions which can be handled by simple to advanced mathematical techniques . Slide40: Mathematical functions processed by mathematical techniques give rise to what is know as a mathematical model essential for communication and connection of mathematics with life-activities and various branches of knowledge . How do we do represent functions? Function or Model: Function or Model Slide44: ii) Functional Notation: Tabular Representation Waste Type (Teku) Waste Type (Sisdol) n n d d Slide45: Formula y = f ( x ) = x. [ x  T = { n , d } , y  S = { n , d } ] Graph A Sequence of Steps: A Sequence of Steps Projected and Proposed Average Waste Generation Quantity ( tons/day): Projected and Proposed Average Waste Generation Quantity ( tons/day ) MATHEMATICAL MODEL: MATHEMATICAL MODEL A Linear Model. Initial Value Problem Initial conditions m = 2.18 and c = 3.08, Equation y = 2.18 x + 3.08 , is the linear mathematical model of KMC - Average Generation Quantity (AGQ) (tons per day in a particular year) A linear model y = ax + b A quadratic model A cubic model A quartic model Trigonometric model Exponential model Logarithmic model A combination or composition of models ( Total area ~ total quantity) Projection of waste generation from 2010 – 2015): A linear model y = ax + b A quadratic model A cubic model A quartic model Trigonometric model Exponential model Logarithmic model A combination or composition of models ( Total area ~ total quantity) Projection of waste generation from 2010 – 2015) Note how a single graph represents all curves that we come across at Higher secondary Mathematics course For all what we have mentioned, we direly need National Principles and Standards: For all what we have mentioned, we direly need National Principles and Standards CATTLE ( Curriculum, Assessment, Teaching, Technology, Learning, Equity) AND CPS (Content and Process Standards) Slide55: Thank You

Add a comment

Related presentations