Math 485 13 Jan 11 Page 1 of 3 Jan 13 2011 Midterm time written progress and presentation on progress End of semester poster session and nal report Assigned a graduate student mentor Must keep him apprised of progress Groups of 3 5 In the rst two weeks do an initial investigation go to references Semester long project on the published papers Everyone must read at least two papers take notes and write a one paragraph summary And work with the group to pick one paper to work on non trivial contents but we need to be actually able to do it Include this debate in the midterm progress report Then carefully work on this paper to understand the math and reproduce the numerical results Reproduce the contents of this paper If the computation power or resources required are too much do a miniature version Then we will be at about spring break and present for an entire class period is to add into the project what we intend to do the end of the poster session Homework weekly Then what do we want to do to improve the project Usually task At the end we need to prepare a poster and a nal report due by See template for poster and past posters Math 485 13 Jan 11 Page 2 of 3 Jan 13 2011 time space relationships helps you anticipate the future very rare that what the mind created on its own is correct a line from negative in nity to positive in nity creates a concept that is generally simpler than the actual idea creates a framework that relates these objects to one another Physical and mental activities the mind directs the physical activities The mind directs the physical through instinct emotion and thought form reasoning The mind has framework that takes in information from the physical The mind creates its own concept image that is stored according to what you see cause and effect The mind creates all kinds of strange and wrong things Human intelligence is greater than that of the animals people understood Products of human intelligence supernatural being will accompany them to war There is one speci c way people understand a relationship numbers to compare the size of different things any physical process you can more or less represent with a number Our abilities are greater in that we can communicate to each other Its not the power of the individual mind its the power of the group the combined intelligence Invent writing now can pass information through time something that animals can not do Many things that human intelligence started are incorrect and con icting Only about 200 300 years ago was the entire world a concept that Many people believe that if they behave a certain way then a many people believe d that the stars foretold the future science and technology Math 485 13 Jan 11 Page 3 of 3 Jan 13 2011 Numbers are related need to describe relationships between quantities Algebra equations come from this and quantities evolve in time giving you the concept of a function now we can describe anything with a function Everyone has a size this size changes as time changes Two basic things size and how fast the size changes most general abstraction Priority of the world in our minds space and time Calculus provides relationship between size time and velocity Says that accumulation of size gives you velocity Integration is summation fundamental relationship revealed relationship between velocity size and the change of size Calculus allows us to describe many natural phenomena Mathematical modeling is using calculus to describe certain natural phenomena Differential equations give information about phenomena No guarantee that the model actually re ects the phenomena Math model is a way our mind creates a framework to understand a natural process and we can see if its good by making predictions Next project will cover mechanical process skipping a stone Later population models pendulum PDE s wave equation Demonstrate how to nd DE s to model the process Try to refresh memory on most relevant mathematics