本科生研究机会
Current undergraduate research opportunities in the Department of 数学ematics 和 统计科学 are described below. For further information, contact the listed faculty member.
Machine Learning in Engineering 和 Biology
Are you interested in the limitless possibilities of Artificial Intelligence 和 want to be at the forefront of cutting-edge technology? Are you eager to develop or apply mathematical knowledge to solve real-world problems? 如果是这样的话, we invite you to join our exciting machine learning projects such as regularized neural networks, 模拟细菌耐药性, or developing topological data algorithms. In addition to the research experience during this project, we offer economic support to develop research activities from our NSF project.
项目的先决条件
强烈的科学抱负, programming skills in Python or willingness to learn them, 大三或大四. Underrepresented minorities in STEM are very welcome to apply.
有兴趣的学生可以联系博士. 巴尔加斯, even if they do not have the listed prerequisites or if they are interested in other applied math topics 和 would like his guidance.
教师联系
埃斯特万的. Hern和ez-巴尔加斯, esteban@salamzone.com，行政长官 Lab of Systems Medicine 和 Infectious Diseases
离散数学
项目描述
This project is in discrete mathematics, particularly in graph theory. The topic is about the existence of substructures of a graph. 给定一个图 G = (v, e) 的订单 n 还有一个子集 W of V ，令的每个顶点 W 至少有2个学位n/3. 的顶点条件 V - W 是未知的. 会有什么影响 W 的结构 G? For example, are there disjoint cycles of G passing through prescribed numbers of vertices of W? 当 W = V ,this topic has been investigated extensively. 当 W 的适当子集是 V, i.e., W 是(或包含在)的子集 V 和 W 不等于 V , this topic is introduced in the following publication:
H. Wang, Partial Degree Conditions 和 Cycle Coverings, Journal of Graph Theory, 78(2015), 295-304.
Substructures other than cycles can be considered as research projects, too. Some weak conditions can be imposed on the vertices which are not in W 为了研究目的.
项目的先决条件
Students should have strong interests in discrete mathematics. It is desirable that students have some knowledge of discrete mathematics, 例如, having taken 数学 176 (离散数学) or other combinatorial courses. It is also desirable that students have taken Calculus I, Calculus II, 和 Linear Algebra.
教师联系
应用线性代数:框架理论
在线性代数中, one of the basic ideas is to express a given object in some space in terms of elements in a representative set like a basis. 当 dealing with different kinds of data sets, the structure of this representative set becomes crucial for efficient storage 和 transmission of data. Frames are representative sets like bases but are redundant. The redundancy allows more flexibility 和 freedom of choice. Frames have now become st和ard tools in signal processing due to their resilience to noise 和 transmission losses.
项目的想法
- Study 和 compare the effect of different kinds of frames in signal (image) reconstruction. Certain frames turn out to be better than others. Determine properties or characteristics of frames that perform better.
- Frame design: In some situations, one might seek a “sparse” representation of a signal. 在其他情况下, one might have to use a subset of a frame to approximate a signal or to deal with loss. 给n the goal, properties like “equiangularity”, “equal-norm”, or “tightness” might be desirable. Consequently, one wishes to construct frames having some “desirable” properties.
- Frame transformations: Starting with a frame, investigate the action of certain “transformations” on the given frame. Which properties of the starting frame are preserved? Determine transformations that can add some property missing in the original frame.
教师联系
Somantika达塔, sdatta@salamzone.com
深度学习
项目描述
Deep learning is a class of machine learning algorithms that use convolutions on a cascade of many layers of nonlinear processing units to extract features from data. It is the current state-of-the-art approach to achieve artificial intelligence, 和 has been successfully applied to a vast variety of difficult tasks. This project aims to get a better underst和ing of the role of convolutions in the deep learning architecture by testing various mathematically-guided designs.
项目的先决条件
Multivariable Calculus (275) 和 Python programming skills.