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This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. It is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability.Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way.

Informed by an integrated critical social semiotic approach, the present critical discourse study investigates the semiotic relations of image–text and the cultural meanings encapsulated in two German language textbooks: Studio d A1 and Netzwerk A1 widely used in Indonesia. Adopting Xiong and Peng's semiotic relation model, the findings demonstrate that Netzwerk A1 provides learners with opportunities to learn, think, and reflect critically on German culture through pedagogical questions regarding image–text‐pedagogy discussion. However, the image–text in Studio d A1 emphasizes the acquisition of linguistic knowledge and does not engage learners in exploring and negotiating their cultural repertoire. This empirical evidence suggests that language textbook writers should consider designing culturally responsive language learning tasks to engage learners in the active construction of cultural knowledge in practice. Any language textbook is always culturally laden, but does it? To which extent can language textbooks convey cultural messages? How do they teach learners cultural knowledge and values? This article presents a critical discourse analysis of cultural representation in German as a foreign language textbooks used in Indonesia from an integrated critical social semiotic perspective.

Neuroergonomics combines neuroscience with ergonomics to study human performance using recorded brain signals. Such neural signatures of performance can be measured using a variety of neuroimaging techniques, including functional magnetic resonance imaging (fMRI), functional near-infrared spectroscopy (fNIRS), and electroencephalography (EEG). EEG has an excellent temporal resolution, and EEG indices are highly sensitive to human brain activity fluctuations. The focus of this systematic review was to explore the applications of EEG indices for quantifying human performance in a variety of cognitive tasks at the macro and micro scales. To identify trends and the state of the field, we examined global patterns among selected articles, such as journal contributions, highly cited papers, affiliations, and high-frequency keywords. Moreover, we discussed the most frequently used EEG indices and synthesized current knowledge regarding the EEG signatures of associated human performance measurements. In this systematic review, we analyzed articles published in English (from peer-reviewed journals, proceedings, and conference papers), Ph.D. dissertations, textbooks, and reference books. All articles reviewed herein included exclusively EEG-based experimental studies in healthy participants. We searched Web-of-Science and Scopus databases using specific sets of keywords. Out of 143 papers, a considerable number of cognitive studies focused on quantifying human performance with respect to mental fatigue, mental workload, mental effort, visual fatigue, emotion, and stress. An increasing trend for publication in this area was observed, with the highest number of publications in 2017. Most studies applied linear methods (e.g., EEG power spectral density and the amplitude of event-related potentials) to evaluate human cognitive performance. A few papers utilized nonlinear methods, such as fractal dimension, largest Lyapunov exponent, and signal entropy. More than 50% of the studies focused on evaluating an individual's mental states while operating a vehicle. Several different methods of artifact removal have also been noted. Based on the reviewed articles, research gaps, trends, and potential directions for future research were explored. This systematic review synthesized current knowledge regarding the application of EEG indices for quantifying human performance in a wide variety of cognitive tasks. This knowledge is useful for understanding the global patterns of applications of EEG indices for the analysis and design of cognitive tasks.

During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration.

Textbooks may reflect a certain ecosophy through the linguistic elements of the content that significantly influences students’ values. This analysis selected 88 discourses from the reading sections of Communicative English for Chinese Learners (Integrated Course), from Books 1 to 4, designed for undergraduate English majors. Based on Systemic Functional Linguistics, the title and the illustration of the reading sections are analyzed to ascertain whether the ideology they reflect is in accord with the ecosophy, that is, the harmonious coexistence of humans, nature, and the development of society. After conducting a textual analysis, all multimodal discourses that can reflect clear ecosophy conform to this idea. Concerning illustrations, seven of them are at variance with the ecosophy. As for the analysis of the logico-semantic relations between image and text, only three discourses are found at variance with the ecosophy, but in actual pedagogical context, these three discourses aim to arouse the thinking of the audience about people’s inappropriate conduct and arouse their ecological consciousness.

Recent fMRI and fTCD studies have found that functional modules for aspects of language, praxis, and visuo-spatial functioning, while typically left, left and right hemispheric respectively, frequently show atypical lateralisation. Studies with increasing numbers of modules and participants are finding increasing numbers of module combinations, which here are termed cerebral polymorphisms—qualitatively different lateral organisations of cognitive functions. Polymorphisms are more frequent in left-handers than right-handers, but it is far from the case that right-handers all show the lateral organisation of modules described in introductory textbooks. In computational terms, this paper extends the original, monogenic McManus DC (dextral-chance) model of handedness and language dominance to multiple functional modules, and to a polygenic DC model compatible with the molecular genetics of handedness, and with the biology of visceral asymmetries found in primary ciliary dyskinesia. Distributions of cerebral polymorphisms are calculated for families and twins, and consequences and implications of cerebral polymorphisms are explored for explaining aphasia due to cerebral damage, as well as possible talents and deficits arising from atypical inter- and intra-hemispheric modular connections. The model is set in the broader context of the testing of psychological theories, of issues of laterality measurement, of mutation-selection balance, and the evolution of brain and visceral asymmetries.

The book presents a unified approach to the perturbation analysis in Matrix Analysis and Control, based on the method of splitting operators and Lyapunov majorant functions. Combined with the Schauder or Banach fixed point principles, this approach allows to obtain rigorous non-local perturbation bounds for a set of important objects in Linear Algebra and Control Theory. Among them are the Schur system of a matrix, the QR decomposition of a matrix, the orthogonal canonical forms of time-invariant linear systems, the state and output feedback gains in pole assignment design, the generalized Schur system of a pair of matrices, the Hamiltonian-Schur and block Hamiltonian-Schur forms of Hamiltonian matrices, and others. In this way, the approach proposed can be used as a unified tool in deriving asymptotic and nonlocal perturbation bounds in matrix analysis and control theory. An important technique of the method considered is the construction of an operator equation, which is equivalent to the perturbed problem. It is based on the splitting of a certain linear matrix operator and its argument into strictly lower, diagonal and strictly upper parts, respectively. This allows to unify the perturbation analysis of matrix problems, involving unitary matrices, in which the resulting matrix is upper triangular. Some other issues such as perturbation analysis of problems with non-unique solution and construction of improved asymptotic perturbation bounds are also considered. The book is intended as a reference in the area of matrix computations and control theory. It will be of interest to researchers in the area of matrix analysis, linear control theory and applied mathematics. The book may also be useful for graduate students in the area of applied mathematics.

The persistent narratives favoring dominant groups make it necessary to investigate the way these groups are portrayed in textbooks, which though they are meant to provide neutral information, often have an agenda that disempowers individuals from marginalized groups. This systemic functional linguistics text analysis of 362 passages of a world history textbook’s sections on African participants asks the following question: How, if at all, does the use of different verb processes position individuals of different ethnic and racial identities? The findings indicate that different processes are used to legitimize European control and other Western involvement in African nations and remove their culpability in the exploitation of African resources. Meanwhile, the textbook authors remove African agency in the time periods following medieval and ancient Africa.