Florian Richter: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Topic: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions 

Speaker: Florian Richter, Northwestern University

June 4, 2020

Ramsey Numbers asymptotics - R(4,t)

An amazing new result

The asymptotics of r(4,t) - by Sam Mattheus and Jacques Verstraete

Random Graphs

Math circle session on random graphs led by Alon Amit at the 2012 Summer BACT

Cellular Automata: Rule 110 + Conway’s Game of Life

"A 1D cellular automaton, Rule 110 (bottom), being fed as input to a 2D cellular automaton, Conway’s Game of Life (top)"

California Approves Revised Math Framework as a Step Forward for Equity and Excellence - July 12, 2023

https://www.cde.ca.gov/nr/ne/yr23/yr23rel54.asp

CDE/SBE Joint Release: #23-54
July 12, 2023

Contact: Communications
E-mail: communications@cde.ca.gov
Phone: 916-319-0818

California Approves Revised Math Framework as a Step Forward for Equity and Excellence

SACRAMENTO—The California State Board of Education today approved the 2023 Mathematics Framework for California Public Schools, instructional guidance for educators that affirms California’s commitment to ensuring equity and excellence in math learning for all students.

“I’m thankful for everyone who worked tirelessly to develop this framework to ensure California’s students have equitable access to rigorous and high-quality math instruction that will prepare them for the future. The framework has struck a great balance in new ways to engage students in developing a love for math while supporting those on an accelerated path,” said Mary Nicely, Chief Deputy Superintendent of Public Instruction. “Our State Superintendent is a champion of equity and excellence, and it is our core mission that every child—regardless of race, ZIP code, or background—has access to a quality education. The approval of the revised Math Framework is one more step forward to meeting the needs of all California’s students.”

The vote today concludes four years of work to update math instructional guidance aligned with the California Common Core State Standards for Mathematics (PDF), which are rigorous learning standards that detail what every student should know and be able to do at every grade level. The framework approved today is the third iteration and reflects revisions responsive to thousands of public comments fielded over two 60-day public comment periods and two public hearings.

The draft was presented by Dr. Mike Torres, Executive Director of the Instructional Quality Commission and a former high school math teacher. Others who participated in the presentation include Dr. Kyndall Brown, Executive Director of the California Mathematics Project at the University of California, Los Angeles; Omowale Moses, Founder and Chief Executive Officer of Math Talks; Dr. Adrian Mims, Founder of The Calculus Project; Ellen Barger, Chair of the Curricular and Improvement Support Committee of the California County Superintendents; and Dr. Linsey Gotanda, Vice Chair of the Instructional Quality Commission.

“This framework provides strategies to challenge, engage, and support all students in deep and relevant math learning by building on successful approaches used in nations that produce high and equitable achievement in math,” said State Board President Linda Darling-Hammond. “It also draws on the experiences of educators who have worked for a decade to develop successful strategies for teaching California’s rigorous standards, carrying those lessons to others across the state. This framework provides teachers and schools with a path to greater excellence with greater equity.”

The guidance includes strategies to:

• Structure the teaching of the state’s math standards around “big ideas” that integrate rather than isolate math concepts—a best practice in high-performing countries.
• Increase focus on developing student mathematical expertise as described in California’s Standards for Mathematical Practice, which include the ability to make sense of problems and persevere to solve them; to reason abstractly and quantitively; to attend to precision; and to apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
• Connect learning to the “real world” through authentic examples and use of data, prompting students to ask and answer meaningful questions. Adding authenticity to lessons helps teachers answer students’ questions around “why do I need to learn this?”
• Allow students to “see themselves” in curriculum and in math-related careers by making math instruction culturally relevant and empowering.
• Stimulate deep learning by sparking student curiosity through lessons that encourage inquiry and problem-solving.
• Ensure that students develop both appreciation of math concepts and fluency in using math efficiently through the productive use of algorithms and mastery of math facts they have come to understand.
• Integrate and align math concepts taught at the elementary, middle, and high school levels.
• Ensure that all high school math pathways are open to all students.
• Support multiple ways to get more students to higher level mathematics—ranging from successful acceleration to differentiated instruction, personalized supports, extra lab sections, and additional coursework offered at multiple junctures—augmenting more effective core instruction.
• Expand high school math course options to encourage more students to go beyond minimum course requirements.
• Encourage students across age spans to become proficient at understanding and using data—a key skill in the 21st century job market.
• Help students to identify misleading uses of data and use data to make decisions in their roles as global citizens.
• Develop in students a “growth mindset” about mathematics, in line with the groundbreaking research of Stanford’s Dr. Carol Dweck, that supports effort and perseverance.
• Instill confidence in learners by dispelling myths about who can and cannot learn math.
• Develop instruction and curriculum that is “multi-dimensional” and employs the use of visuals, graphics, and words in addition to numbers and equations.

More information is available on the California Department of Education's Mathematics Frameworks web page, which includes frequently asked questions, an overview, and a timeline of events in the framework’s development.

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Tony Thurmond — State Superintendent of Public Instruction
Communications Division, Room 5602, 916-319-0818, Fax 916-319-0100

Last Reviewed: Wednesday, July 12, 2023

Peter Sarnak on Möbius Disjointness

Senior Capstone presentations - May 10, 2023

Session of Senior Capstone presentations today at ONU, featuring topics on Partial Differential Equations and Number Theory. It was definitely a success, with a lively attendance. Many thanks to these awesome students!

The Patterns in the Primes, with Andrew Granville

 

The Search for Randomness | Jean Bourgain

 

More teaching chalkboards

Chinese Remainder Theorem...

Number theory and cryptography class - chalkboard pictures

Today, the topic was the Euclidean algorithm...

Just before erasing this number theoretic Tibetan mandala :)