A Common Vision for the Undergraduate Math Program in 2025: Our Role Friday 2:00 – 2:50 S112

Presenters today include: Julie Phelps Rob Kimball Rob Farinelli A Common Vision for the Undergraduate Math Program in 2025: Our Role

Goals of this session: Encourage you to take steps to modernize the undergraduate mathematics curriculum. Share the COMMON VISION.

Why do you teach the content you now teach?

A Common Vision Discrete Time Difference Equations Recurrence Relations

A Common Vision In 1202 the Italian Fibonacci published Liber Abaci which contained the difference equation that models the population growth of rabbits.

A Common Vision for the Undergraduate Math Program in 2025

Funded by the National Science Foundation. PI: Karen Saxe Co-PI: Linda Braddy Web: The Leadership Team Karen, Linda, John Bailer, Rob Farinelli, Tara Holm, Vilma Mesa, Uri Treisman, Peter Turner A Common Vision for the Undergraduate Math Program in 2025

A Common Vision modernize the undergraduate mathematics program The primary goal is to develop a SHARED VISION in the mathematical sciences community of the need to modernize the undergraduate mathematics program, especially the first two years. collective action It is time for collective action to coordinate existing and future efforts … to improve undergraduate education in the mathematical sciences.

A Common Vision The crisis in mathematical sciences education is well documented in high-profile reports such as the U.S. government’s PCAST report on STEM education and the National Academies’ report on The Mathematical Sciences in PCAST report on STEM educationThe Mathematical Sciences in 2025 Committee on the Undergraduate Program in Mathematics Curriculum Guide Committee on the Undergraduate Program in Mathematics Curriculum Guide Modeling Across the Curriculum Undergraduate Degree Programs in Applied Mathematics Partner Discipline Recommendations for Introductory College Mathematics Beyond Crossroads Guidelines for Undergraduate Programs in Statistical Science Guidelines for Assessment and Instruction in Statistics Education

A Common Vision “One of the most striking findings is that all seven guides emphasize this point, in particular: The status quo is unacceptable The status quo is unacceptable.” Committee on the Undergraduate Program in Mathematics Curriculum Guide Committee on the Undergraduate Program in Mathematics Curriculum Guide Modeling Across the Curriculum Undergraduate Degree Programs in Applied Mathematics Partner Discipline Recommendations for Introductory College Mathematics Beyond Crossroads Guidelines for Undergraduate Programs in Statistical Science Guidelines for Assessment and Instruction in Statistics Education

A Common Vision Common themes in all the guides: Curriculum More pathways Modeling and computation Connections to other disciplines Communication Transitions Course Structure Pedagogy Technology Workforce Preparation Faculty Development and Support

A Common Vision Predictive Analytics Predictive analytics is the practice of extracting information from existing data sets in order to determine patterns and predict future outcomes and trends.

A Common Vision Predictive Models Descriptive Models Decision Models Analytical Customer Relationship Management (CRM) is a frequent commercial application of Predictive Analysis.

A Common Vision Predictive Models Descriptive Models Decision Models Predictive analytics can help analyze customers' spending, usage and other behavior, leading to efficient cross sales, or selling additional products to current customers

A Common Vision FORBES: $16.1 Billion Big Data Market: 2014 Predictions From IDC And IIA Growing 6 times faster than IT market Employees work in teams and establish best practices using operationalizing and management models Talent Shortage: over 100 programs at universities exist where analytics and data sciences “are in focus”

A Common Vision Geospatial Analytics See patterns and trends in a recognizable geographic context, so they're easier to understand and act upon. Anticipate and prepare for possible changes due to changing spatial conditions or location-based events. Develop targeted solutions to business challenges that may require different responses in different locations.

A Common Vision Geospatial Analytics

Each red dot represents at least one student and is denoted by a POINT in the student layer. The student layer contains geographic as well as academic data about each of the 17,572 K-12 students.

Queries Into Big Data - Attribute Table IDSchoolGradeStreet #StreetFRLAGEOG East3132Adam West114234Booker West9324Carlton East4144David South623Eden South1242Frank005 Grade 5 AND (FRL=1 OR AG=1)

Queries Into Big Data - Visual Representations of Data

Median Income (ACS 2011)

A Common Vision Report to the President Engage to Excel: Producing one million additional college graduates with degrees in science, technology, engineering, and mathematics (February 2012) Three imperatives underpin this report: Improve the first two years of STEM education in college Provide all student with the tools to excel. Diversify pathways to STEM degrees

A Common Vision The Mathematical Sciences in

A Common Vision Chapter 2 - VITALITY OF THE MATHEMATICAL SCIENCES The Topology of Three-Dimensional Spaces Uncertainty Quantification The Mathematical Sciences and Social Networks The Protein-Folding Problem The Fundamental Lemma Primes in Arithmetic Progression Hierarchical Modeling Algorithms and Complexity Inverse Problems: Visibility and Invisibility The Interplay of Geometry and Theoretical Physics New Frontiers in Statistical Inference Economics and Business: Mechanism Design Mathematical Sciences and Medicine Compressed Sensing

A Common Vision Chapter 3 - CONNECTIONS BETWEEN THE MATHEMATICAL SCIENCES AND OTHER FIELDS Chapter 4 - IMPORTANT TRENDS IN THE MATHEMATICAL SCIENCES

A Common Vision Research in the Mathematical Sciences is on a ROLL The vitality of the U.S. mathematical sciences enterprise is excellent.

A Common Vision Market Basket Analysis (Recommender Theory) How Does Amazon Know What You Want?

A Common Vision Market Basket Analysis (Recommender Theory) How Does Amazon Know What You Want?

A Common Vision Multi-objective Optimization Optimization is an important mathematical topic. But, let's be honest; many of the problems we assign in a calculus text are based on what someone else is doing; e.g., find the optimal amount of a product to produce. Many real scenarios are based on what others are doing or producing. This slides into a "multiple optimization" problem where what I do influences what you have to optimize and what you do determines what I have to optimize.

A Common Vision Multi-objective Optimization Multi-objective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. Example problems include analyzing design tradeoffs, selecting optimal product or process designs, or any other application where you need an optimal solution with tradeoffs between two or more conflicting objectives.

A Common Vision Design Decisions Aspect Ratio Dihedral Angle Vertical Tail Area Engine Thrust Skiin Thickness # of Engines Fuselage Splices Suspension Points Location of Mission Computer Access Door Location F/A-18 Aircraft Objectives Speed Range Payload Capability Radar Cross Section Stall Speed Stowed Volume Acquisition Cost Cost/Flight Hour Engine Swap Time Assembly Hours MAX MIN

A Common Vision The Mathematical Sciences are being used everywhere Mathematical sciences work is becoming an increasingly integral and essential component of a growing array of areas of investigation in biology, medicine, social sciences, business, advanced design, climate, finance, advanced materials, and much more.

A Common Vision Useful mathematics in R & D Modeling and Simulation Mathematical Formulation of Problems Algorithm and Software Development Problem-Solving Statistical Analysis Verifying Correctness Analysis of Accuracy and Reliability Explaining and modeling complex phenomena with mathematics

A Common Vision Two major drivers in the expanding role of the mathematical sciences: The ubiquity of computations simulations – they build on concepts and tools from the mathematical sciences Exponential increases in the amount of data available for many enterprises The Internet, which both creates data and makes large quantities of data readily available, has magnified the impact of these drivers.

A Common Vision The changing role of mathematics impacts what mathematics/statistics students need. Motivate math by how it is used…in other disciplines Incorporate multiple modes of mathematical thinking Provide new entry-points and new pathways Partner with other disciplines to create a compelling menu of lower-division courses Diversify teaching methods, engage with online education Share in a community-wide effort to bring successful experiments to scale

A Common Vision Evolutionary Game Theory Evolutionary game theory originated as an application of the mathematical theory of games to biological contexts, arising from the realization that frequency dependent fitness introduces a strategic aspect to evolution. Recently, however, evolutionary game theory has become of increased interest to economists, sociologists, and anthropologists--and social scientists in general--as well as philosophers.

A Common Vision “The real value of de Mesquita’s” work is not only in his predicting how a corporate event might unfold. It is also in figuring out how to influence that event. New York Times article about Bruce Bueno de Mesquita – one of the world’s most prominent applied game theorists.

What would it take to modernize / update the undergraduate mathematics curriculum?

From the INGenIOuS Report: We acknowledge that changing established practices can be difficult and painful. Changing cultures of departments, institutions, and organizations can be even harder. But there is reason for optimism.

WAKE UP Change is unquestionably coming to lower- division undergraduate mathematics, and it is incumbent upon the mathematical sciences community to ensure that it is at the center of these changes and not at the periphery. VISION is a community-wide effort to cooperatively spark improvement.

Our Role AMATYC Inform members about the VISION project through Affiliates Publications Academic Committees The recommendations of the Vision report will influence the Update of C ROSSROADS New AMATYC Strategic Plan

Our Role You Read the publications mentioned in this presentation Keep up with the VISION Initiative Rethink the curriculum Rethink how you teach Work with colleagues (in your school and/or affiliate) to take steps to modernize the curriculum

Thanks A thank you to Ben Braun, Mark Green, Ron Rosier, and Don Saari for helping with materials for this presentation.

A Common Vision

T OPICS THAT DESERVE MORE ATTENTION Predictive Analytics – Data analysis – Modeling and Simulation – Algorithms Recursive Equations Probabilistic and Statistical Thinking Optimizing Game Theory Topology Graph Theory

A Common Vision Algebraic Topology Aspects of algebraic topology (e.g., index theorem, fixed point theorems) are often used in economics (for instance, to prove the existence of equilibria) and they are beginning to be used in psychology. Indeed, part of Kenneth Arrow's Nobel in Economics was based on his using fixed point theorems to prove the existence of a price equilibrium. He used the techniques developed by John Nash to prove the existence of equilibria in game theory.

A Common Vision Graph Theory and Network Theory Graph theory and network theory is a fast growing area in sociology, management sciences, and other social sciences. It is even being used to understand connections between crimes and trends in terrorism. In fact, a recently developed procedure currently places about a million students each year into the appropriate math class: ALEKS. ALEKS was discovered and developed by a mathematical psychologist

A Common Vision Functional Equations: F(g(x), x) = g(f(x)) Functional equations are very big in cognitive psychology. Experiments with human subjects define the functional relations; the mathematics of functional equations define the functions and resulting theory. A sizable portion of Duncan Luce's work depends on this approach.