analysis and recursive analysis, among others. Shindler et al. [12] perform a replication study of [19] that targeted misconceptions about dynamic programming. Özdener [9]'s study identifies students' misconceptions about time-efficiency of algorithms, while Velázquez-Iturbide [16]'s work addresses misconceptions about optimization problems and their corresponding algorithms.

Other research related to algorithms concerned effective teaching and evaluation strategies [5,11,18] and means to incorporate responsible-computing content into the course structure [6].

More relevant to our work is the study conducted by Hertz [7]. Their survey was focused on CS 1 and CS 2 course topics, whereas our survey concerned all algorithms course topics. Similar to our own work, they found significant divergence between courses.

The first step of our data collection process entailed creating a (noncomprehensive) list of academic institutions to include in the study. We only included universities in the United States that had a 4-year computer science (or related) program. We also ensured that each of the 50 states was represented, at least to some extent.

Once our list of institutions had been constructed, we began examining the catalog descriptions of undergraduate courses at each institution in order to identify a suitable course. If the course title indicated the class was introductory and solely an algorithms course (e.g., łDesign of Algorithms, ž łAnalysis of Algorithms, ž łFundamental Algorithms,ž etc.), we included it. Otherwise, if there was no such course, we would include another course with łalgorithm(s)ž in the title so long as there was evidence that at least one topic from the ACM's łAlgorithmic Strategiesž was included. This condition was most often applied to łData Structures and Algorithmsž courses, which were often a terminal algorithmic course.

After creating lists of undergraduate algorithms courses, for each course, we compiled a list of up to three instructors who had taught it within the past 2 years. To find the instructors for each course, we applied a variety of methods. The most common way was through looking at publicly viewable course schedules which list instructors' contact information, though other sources were employed, such as course websites. After finalizing the list of emails, we sent an invitation to participate in the survey to all instructors in that email list. Each survey respondent was offered a $25 Amazon gift card for completing the survey.

When designing the survey, our goal was to gain insight into both the course structure and the topics typically taught. The survey contained two main parts. The first, consisting of three sections, focused on the organization of the course. These sections ask about general course details, such as grading breakdowns, dedicated class section times, programming assignments, written assignments, and in-class assessments (exams and quizzes).

One of our motivations behind these questions was to determine emphasis on the theoretical components versus applied components of the courses. As such, we asked questions about both the content and number of assignments.

In the second part, based on the core topics from the ACM Computer Science Curricula 2013 [8], we asked where the topic is first taught (i.e., prerequisite course, the algorithms course in question, other elective or required courses, nowhere in the curriculum, unsure, or other). Multiple core topics under Basic Analysis were combined into the topic łAsymptotic Analysisž to simplify and shorten the survey length. Similarly, we included an abridged version of the Proof Techniques section from the Discrete Structures knowledge area to identify how proofs were integrated into the course. The łBasic Automata, Computability and Complexityž and łAdvanced Data Structures, Algorithms, and Analysisž sections were preceded by a question on whether the instructor taught any topics that could fall under either section and if not, the section was skipped.

Finally, we asked three open ended questions, on issues encountered, desired course changes, and any other comments.

The most significant threat to the validity of our survey is in the selection process of courses and institutions. In the first wave, we selected the initial universities ourselves. As such, the first institutions we reached out to were more often well-known universities. Our second and third waves addressed this problem by attempting to be almost fully comprehensive in previously uncovered states along with a few other states. However, it should be noted that this means we do not have a perfectly random sample. Secondly, while łproperly titledž introductory courses would always be surveyed, programs that didn't have such a course were only surveyed if they included a topic from łAlgorithmic Strategies. ž This criterion, however, may cause some confirmation-bias, since this pre-supposes that algorithms courses need to cover these strategies.

Another threat comes from the six adjunct respondents. While adjuncts likely know the course they are teaching very well, it is possible that they are less familiar with the general curriculum of the institution as a whole. A survey by the TIAA Institute indicates around 23% of adjuncts have jobs outside of academia, and 26% teach at multiple institutions [17]. As such, this could lead to certain information being omitted or misrepresented.

Finally, there are threats related to doing surveys. All of the data is given voluntarily by those who responded, which can bias the sample. There can be errors when filling out surveys. For ours particularly, we allowed the final two sections to be skipped if the instructor indicated they did not teach any topic in the section. It could be that in these cases, the topics are taught in different locations at these universities. There is also the issue of sample size; we only received responses from 87 instructors.

Our initial list had 615 higher-education institutions. Of these, 495 had a 4-year computer-science adjacent program, and 373 of those had an applicable algorithms course. From this, we were able to send out emails to 411 instructors from 302 institutions whose contact information we were able to find. We were able to gather responses from 87 instructors across 79 institutions in 34 states. 57 of these responses were from doctoral universities with 36 being from an R1 university, 12 from an R2 university, and 9 from a doctoral/professional university as defined by the Basic Carnegie

When teaching algorithms, by far the most common issue instructors reported facing was insufficient background on prerequisite concepts, with 54 of the 80 (68%) responses to Q1 exhibiting this (Theme 1). 40 out of those 54 (74%) made references to students' weak foundation in mathematics and proof-writing. Only nine responses (17%) expressed concern with a lack of programming skills to properly implement algorithms (the final 10 responses (19%) not elaborating on the prior knowledge students were lacking).

Another concern raised was the assessment of students' algorithm design skills (Themes 4 and 7). Instructors frequently commented on the difficulty in creating assessments and assignments for students to apply their knowledge in designing algorithms. A key difficulty is to come up with novel problems, unique from those discussed online. Another is that some students are unable to apply algorithm design beyond problems encountered in class.

Respondents also noted the abstract nature inherent in learning these topics as a struggle. Themes 5 and 6 illustrate this as instructors note students' struggles in recognizing the importance of algorithms and their relevance with real-world applications. Some instructors listed particular algorithmic concepts that students had trouble with as well, most commonly dynamic programming, greedy algorithms, and NP-completeness.

Of the 46 responses we collected for Q2, we witness two categories of themes: those expressing desires to add to the course in some way, like adding more material, emphasizing particular topics, or providing more opportunities to apply what they learned (Themes 6, 9, 10) and those which seek to address the difficulty of the course by reducing the amount of material covered or ensuring prerequisite courses cover the concepts needed (Themes 7 and 8).

We looked to see if there were any associations between the survey variables and additional data we collected on the institutions we surveyed 5 . We also used our previous categorization of instructors' research in algorithms or non-algorithms adjacent research as a variable. We obtained these associations by calculating the Cramér's V measure for each pair of variables 6 . We found that there are some moderate associations between variables from the same sections of the survey. We first see this with the variables from the łEvaluation of Student Masteryž sections where question types on the homework and exams were correlated with one another. Likewise, for the Fundamental DSA topic section, there are moderate associations between quadratic sorting algorithms, hash tables, binary trees, and heaps, having Cramér's V values in the range 0.18 and 0.55. On the other hand, graph representations, depth-and breadth-first search, shortest-path algorithms, and minimum spanning tree algorithms, the most common topics from the DSA section, have Cramér's V measures less than 0.13 with the other topics (and associations between 0.13 and 0.78 amongst the topics). Given these observations, it is possible that the łtypicalž DSA topics concern tree traversal and graph algorithms. Furthermore, 𝑂 (𝑛 log 𝑛) sorting algorithms are the only DSA topic that has any moderate associations with any Algorithmic Strategic topics, most notably having an Cramér's V score of 0.34 with divide-andconquer, suggesting 𝑂 (𝑛 log 𝑛) sorting algorithms may be covered to serve as examples for algorithmic paradigms. For the advanced algorithms topics, they have moderate intra-associations and weak inter-associations, possibly implying these topics are rarely covered together. Balanced trees, graph-theoretic algorithms, and network flow, which show up in a higher percent of algorithms/prerequisite courses, have less association with the other advanced topics.

We did not find any high associations between institution data and instructor's research area and our survey variables, suggesting that algorithms course structure and topics are not particularly dependent institution type or professor research background.

A more focused survey could expand upon the themes we derived. Other research could look for and apply solutions to these issues. Finally, conducting surveys in other areas can further increase our understanding of the current state of CS education.

In this study, we found that while instructors often use the term łalgorithmsž to refer to a specific course, the actual course being referenced has a large variation between academic institutions: it can be oriented around mathematics, programming, or somewhere in between. Even within these divisions, instructors often select very different subsets of topics. In addition, instructors regularly feel students are unprepared for their courses and have a variety of new directions they wish to take it -whether to focus on certain course topics or to make the class more or less mathematical.

As educators and researchers, we need to take into account the diversity in how algorithms courses are taught. Future studies should keep this in mind, and either make efforts to be applicable to a variety of courses or be tailored to a specific version of the course. When interacting with new transfer students or graduate students, we should be careful not to make assumptions about the topics covered in prior algorithms courses. Finally, as educators, we should make use of this heterogeneity to pull elements from other courses into our own to continue to improve and refine.