This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Antimicrobial resistance is a looming threat to global health. As a result, the livestock industry is moving away from using antibiotics in feed to enhance growth. But this shift may have led to increased rates of systemic infections and reduced production efficiency. Alternatives for antibiotic growth promotants (AGPs) are needed, but the mechanism behind the efficiency of AGPs is largely unknown. So, a recent study systematically evaluated the composition and function of the chicken gut microbial community in response to AGPs. The impact of AGPs was dependent on the birds' age and diet as well as the intestinal sampling location. Overall, AGPs had a limited impact on the abundances of specific microbial groups but did shift which groups were influential and exclude others. The chicken gut microbiome functionally responded to AGPs by changing the expression of multiple pathways, including by increasing expression of cell wall formation and antimicrobial resistance mechanism genes..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Bacteria and other microorganisms cover nearly every surface on earth, including the surfaces we build and maintain. Ocean piers are unique sites at the intersection of terrestrial, aquatic, and human-built environments. Saltwater spray, inclement weather, and pollutants make piers a harsh environment for bacteria. Together, these factors suggest that piers house a unique microbiome. Researchers recently conducted a study to characterize the microbiomes found on pier surfaces. On nine piers along the coast of Hong Kong, the researchers found diverse microbiomes that were rich in novel bacterial species. Surface material (metal versus concrete) was the strongest factor influencing the bacterial community structure. Although the overall abundance was low, corrosion-associated bacteria were more prevalent on metal surfaces, and high-touch surfaces like handrails and poles had more human skin-associated microbes than other surfaces..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

As taught in 2006-2007 and 2007-2008.

Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.

This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include:

– norm topology and topological isomorphism;
– boundedness of operators;
– compactness and finite dimensionality;
– extension of functionals;
– weak*-compactness;
– sequence spaces and duality;
– basic properties of Banach algebras.

Suitable for: Undergraduate students Level Four

Dr Joel F. Feinstein
School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.

This is a module framework. It can be viewed online or downloaded as a zip file.

As taught Autumn semester 2010.

Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.

This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include:

– norm topology and topological isomorphism;
– boundedness of operators;
– compactness and finite dimensionality;
– extension of functionals;
– weak*-compactness;
– sequence spaces and duality;
– basic properties of Banach algebras.

Suitable for: Undergraduate students Level Four

Dr Joel F. Feinstein
School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

This engineering design challenge is a great hands-on activity that utilizes the engineering design process, 3D modeling, and 3D printing technology. The challenge can be completed individually or in groups of 2 to 3. Students will work to complete the following challenge: Using the design process, design, document, model, and produce a toy car with interchangeable parts.

With an emphasis on teaching and learning, this book is for an advanced undergraduate course on partial differential equations or a beginning graduate course on partial differential equations. Divided into 13 chapters, this textbook covers most of the important topics found in books on partial differential equations, using most of the time the same approach.

This book contains material on partial differential equations usually taught at the undergraduate level for science and engineering students. The reason for including this material is that many mathematics students do not have the chance to study partial differential equations at the undergraduate level. The sections covering the undergraduate material are accessible to readers with only a calculus background. The presentation in these sections is usually more formal and therefore appropriate for introducing partial differential equations for science and engineering students. This book is accessible to students with a minimal introduction to measure and integration, and functional analysis

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Solving problems doesn’t always require an entirely new fix -- or new software. A team at IBM recently demonstrated that repurposed software offers improved functional characterization of microbiomes at a fraction of the development time. Currently, microbial functional profiling is typically done by classifying sequencing reads taxonomically, followed by computationally demanding functional analysis. But in a clever twist, researchers opted instead to directly compare sequencing reads to a functionally annotated database. The group developed a tree-shaped functional hierarchy and repurposed taxonomic bioinformatics tools to do the functional annotation. The method was applied to soil samples taken across the globe. This revealed, for example, that antioxidant activity was much higher in polar regions compared with equatorial areas. Next, the team plans to use the technique on other biological samples to further probe the secret lives of microbes..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.